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SPIRALS    IN   NATURE   AND 
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SPIRALS 
IN    NATURE    AND    ART 


A  STUDY  OF  SPIRAL  FORMATIONS  BASED  ON  THE 
MANUSCRIPTS  OF  LEONARDO  DA  VINCI,  WITH 
SPECIAL  REFERENCE  TO  THE  ARCHITECTURE 
OF  THE  OPEN  STAIRCASE  AT  BLOIS,  IN  TOURAINE, 
NOW  FOR  THE  FIRST  TIME  SHOWN  TO  BE 
FROM  HIS  DESIGNS,  BY  THEODORE  ANDREA 
COOK,  M.A.,  F.S.A.,  AUTHOR  OF  "OLD  TOURAINE," 
"ROUEN,"  ETC.,  ETC.,  WITH  A  PREFACE  BY  PRO- 
FESSOR E.  RAY  LANKESTER,  F.R.S.,  ETC.,  DIRECTOR 
OF  THE  BRITISH  MUSEUM  OF  NATURAL  HISTORY 


WITH    ILLUSTRATIONS 


LONDON 
JOHN    MURRAY,   ALBEMARLE   STREET,   W. 

1903 


76 


Hfi 


CONJUGI   CARISSIMAE 


PREFACE 


I  have  often  thought  that  if  the  public  knew 
more  of  the  real  beauties  of  Nature,  our 
Museums  would  be  far  more  thronged  with 
visitors  than  is  the  case  at  present.  Every 
effort  is  made  in  many  of  them  to  display  the. 
various  specimens  to  their  best  advantage,  and 
to  explain  clearly  what  they  are.  But  some- 
thing more  is  often  needed,  and  the  man  who 
knows  most  about  these  matters  is  not  always 
the  man  who  has  time  to  write  about  them. 
Moreover,  the  writings  of  the  specialist  are  too 
often  necessarily  expressed  in  language  that 
is  fully  intelligible  only  to  a  few.  Yet  if  the 
energetic  worker  in  other  fields  will  pause  a 
while  to  consider  what  he  can  learn  from 
biology  or  botany,  he  will,  I  think,  be  rewarded 
far  beyond  his  expectations. 

Leonardo  da  Vinci  was  one  of  the  few  men 


x  PREFACE 

who  can  be  great  in  several  directions.  His 
painting  would  have  sufficed  alone,  and  by  it 
alone  he  is  too  often  judged.  But  he  was  a 
man  of  science,  an  engineer,  a  mathematician, 
a  biologist,  as  well ;  and  his  leisure  was  given 
to  sculpture  and  to  architecture. 

Never  has  so  much  talent  been  united  in  one 
man.  Yet  modern  men  of  art  and  science, 
who  have  specialised  on  their  own  subjects, 
may  derive  great  benefit  from  the  work  of 
other  specialists  in  these  days  when  it  is  practi- 
cally impossible  to  keep  abreast  of  one  line  of 
research  without  an  exclusive  devotion  to  its 
progress. 

As  far  as  I  am  aware,  Mr  Theodore  Cook 
has  not  specially  devoted  himself  to  any  of  the 
scientific  subjects  which  come  under  the  scope 
of  his  present  inquiry.  He  is  perhaps  known 
to  a  few  as  the  historian  of  some  districts  in 
France.  But  his  name  is  unfamiliar  to 
students  of  biology  and  mathematics.  The 
training  which  he  received  in  Paris — a  training 
which  I  could  wish  were  more  appreciated  at 
our  own  Universities — has  emboldened  him  to 
enter  upon  a  course  of  speculative  generalisa- 
tion which  a  more  restricted  method  of  study 
might   have   prevented.      He   looks,  in   fact, 


PREFACE  xi 

upon  the  results  of  others'  labour  with  a  mind 
that  is  more  ready  to  perceive  its  general  value 
than  are  those  intellects  which  have  concen- 
trated a  unique  energy  upon  a  single  set  of 
problems. 

I  have  perused  with  the  greatest  interest 
many  of  those  manuscripts  of  Leonardo  on 
which  Mr  Cook's  work  for  this  Essay  has  been 
primarily  based.  I  also  know  many  of  the 
steps  he  has  taken  to  arrive  at  his  conclusions, 
and  among  them  I  would  point  out  the  com- 
parisons suggested  in  the  growth  of  horns,  as 
shown  in  figs.  17,  18,  19  and  20 ;  and  the  col- 
lection of  various  shells,  made  to  investigate 
the  growth  of  plaits  upon  the  columella,  as 
seen  in  the  series  illustrated  by  figs.  52,  27,  30, 
7,  53,  31,  32,  and  33.  These,  it  seems  to  me, 
will  be  distinctly  useful  to  the  biologist,  apart 
from  any  connection  in  which  they  may  be 
found  in  these  pages. 

The  hope  that  mathematicians  may  in  time 
produce  a  system  of  definitions  that  will  be  of 
use  both  to  the  biological  and  to  the  artistic 
morphologist,  is  by  no  means  new.  But  every 
fresh  instance  that  tends  to  make  it  more 
probable  must  contribute  to  the  advantage 
alike  of  science  and  of  art.    I  am  perhaps  not  so 


xii  PREFACE 

much  interested  in  the  attribution  of  a  certain 
staircase  to  Leonardo  as  I  am  in  the  steps  by 
which  Mr  Cook  seeks  to  enforce  a  theory  that 
is,  after  all,  susceptible  neither  of  proof  nor  of 
disproof.  Yet  I  feel  that  architecture,  if  it  is 
to  appeal  to  all  of  us,  as  it  should  do,  must,  in 
the  end,  be  based  upon  some  general  morpho- 
logical principles.  I  have  long  looked  in  vain 
for  any  architectural  hand-book  that  would  not 
merely  suggest  the  foundations  on  which  build- 
ing and  ornament  finally  rest,  but  would  also 
lucidly  explain  to  the  untechnical  observer  the 
reasons,  the  faults,  or  the  virtues  of  any  archi- 
tectural example  with  which  he  might  be 
brought  in  contact. 

That  there  are  certain  natural  laws  which 
bind  the  work  of  the  architect  as  they  must 
bind  the  growth  of  all  organic  structure,  is 
evident.  Mr  Cook  has  suggested  one  of  them, 
and  his  suggestion  involves,  it  seems  to  me, 
a  course  of  inquiry  that  would  prove  as  service- 
able to  the  builder  as  it  should  be  fruitful  to 
the  biologist. 

The  scientific  reader  will  not  need  to  be 
warned  against  certain  generalisations  which 
Mr  Cook  has  formulated  upon  what  are  con- 
fessedly insufficient  data.    But  I  am  not  aware 


PREFACE  xiii 

that  he  has  indicated  anything  that  is  in  itself 
improbable,  or  that  may  not  be  eventually 
rendered  possible  when  the  scope  of  our  experi- 
ence and  knowledge  is  enlarged  by  further 
study.  The  investigation  of  spiral  forms  in 
Nature  is  itself  a  department  of  scientific 
inquiry  that  is  still  very  incomplete,  and  I 
believe  I  am  correct  in  thinking  that  neither 
in  mathematics  nor  in  architecture  has  the  last 
word  yet  been  said  upon  this  interesting 
subject.  There  are  many  gaps  in  Mr  Cook's 
argument  which  may  doubtless  be  filled  up 
by  existing  knowledge ;  but  there  are  many 
more  which  await  investigation,  and  he  has  at 
least  indicated  one  way  in  which  their  value 
may  be  at  once  put  to  a  practical  test. 

The  example  of  Leonardo  will  be  difficult 
to  follow  until  a  man  like  Leonardo  reappears. 
Nature  seems  to  have  broken  the  mould,  and 
its  fragments  have  been  buried  beneath  com- 
petitive examination  papers.  But  when  to  a 
creative  imagination  which  approaches  his, 
shall  be  added  a  knowledge  of  Nature  that 
may  well  be  greater,  then  every  branch  of 
intellectual  activity  will  benefit,  even  if  the 
immediate  result  be  not  all  that  Leonardo 
hoped  for  when  he  wrote,  so  many  centuries 


xiv  PREFACE 

ago :  "  In  this  the  eye  surpasses  Nature, 
inasmuch  as  the  works  of  Nature  are  finite, 
while  the  things  which  can  be  accomplished 
by  the  handiwork,  at  the  command  of  the  eye, 
are  infinite." 

E.  Ray  Lankester. 


CONTENTS 


PAGE 

Preface.     By  E.  Ray  Lankester        .        .  vii 

CHAPTER  I 

the  argument. 

Sympathy  with,  many  things  as  essential  as  specialism 
in  a  few — The  secrets  of  Voluta  vespertilio — Archi- 
tectural theory — The  Open  Staircase  at  Blois — The 
Manuscripts  of  Leonardo — The  "  Italian  brother  of 
Faust " — Rodin's  Creed — Discoveries  of  Leonardo  1 

CHAPTER  II 

OF   SPIRALS. 

Right-  and  left-handed  spirals — The  Prentice's  Pillar — 
Columns  at  Canterbury — Screws  and  shavings — 
Celtic  torques — Left-handed  men — Narwhal's  tusks 
— An  Elephant's  tusk  —  Helicoprion  —  Turbinella 
rapa,  the  Indian  Chank  shell — Spiral  ornament — 
Helicteres  ixora — Lanistes — A  return  to  Nature         .  26 


xvi  CONTENTS 

CHAPTER  III 

OF   PLANTS. 

PAGE 

"Lady's  Tresses" — Pine  cones — Palms — The  Devil's 
Corkscrews — Twining  plants — Tendrils — Mr  A.  H. 
Church  and  Phyllotaxis — The  Logarithmic  Spiral  54 


CHAPTER  IV 

OF   SHELLS. 

Vorticella — Stentor — Dr  George  Wherry  and  the  growth 
of  horns — Errors  in  argument — Spiral  twists  and 
spiral  curves — Bypaths  of  research— Spiral  growth 
in  shells — Sinistral,  dextral,  and  "  ultra-dextral " 
shells — Ammonite  and  Nautilus      .        .        .        .  73 


CHAPTER  V 

COMPARISONS. 

Scalaria  scalaris  and  the  Palazzo  Contarini,  Venice — 
Wrong  uses  of  spiral — Mitra  papalis  and  Escalier  de 
la  Heine  Berth  e,  Chartres — Telescopium  telescopium 
and  the  old  Staircase  at  Blois 94 


CHAPTER  VI 

A   VANISHED   ART. 

Constructive  and  deliberate  "  asymmetry  "—Delicate 
irregularities  in  line  —  Discovery  of  curves  in 
Egyptian  and  Greek  Architecture — Evelyn  in  old 
St  Paul's — "  Symmetrophobia "  according  to  Pro- 
fessor Goodyear  —  The  Campanile  at  Pisa  not 
accidental — What  we  lose  by  mathematics      .        .  100 


CONTENTS  xvii 


CHAPTER  VII 

THE   NAUTILUS. 

PAGE 

Plaits  on  the  columella  of  shells — Tracheae  of  insects 
and  spiral  tubes  in  plants — A  series,  to  show  the 
formation  of  the  columella,  from  Turritella  lenti- 
ginosa  to  Voluta  musica — Sir  John  Leslie,  Canon 
Moseley,  and  the  Nautilus — Professor  Goodsir  and 
the  Logarithmic  Spiral — M.  Vial  de  Saint-Bel  and 
the  race-horse  "  Eclipse  "—Prof  essor  Weldon  and 
Clausilia  laminata— Pasteur     .         .         .         .        .  115 


CHAPTER  VIII 

OF   MASONRY. 

Evolution  of  the  spiral  staircase  in  the  Feudal  Keep — 
The  steps  that  lead  to  Hell — Appearance  of  the 
central  shaft — Tower-houses  and  Newel-staircases — 
A  delicate  problem  in  construction — The  jest  of 
Chambord — Left-  or  Right-handed,  "  dexiotropic  " 
or  "leiotropic?" 132 


CHAPTER  IX 

THE   EXILE. 

Leonardo  da  Vinci  at  Amboise — Ludovico  Sforza  at 
Loches,  and  Caesar  Borgia  at  Chinon  and  Blois — 
Clos-Luce — The  grave  at  Amboise — Researches  of 
Leonardo — Botany — Architecture — Flight  of  birds 
— Hydraulics — Head-dress  for  "Leda" — Shells — 
The  Amboise  Stair  and  Turritella — The  Blois  Stair 
and  Telescopium 146 


xviii  CONTENTS 


CHAPTER  X 

THE   SHELL    OF    LEONARDO. 

PAGE 

The  Open  Staircase  in  the  wing  of  Francis  I.  at  Blois 
— Its  exterior  and  interior — Valuta  vespertilio — Its 
exterior  and  interior — Its  rare  and  common  forms 
— Agreements  and  differences — The  staircase  a  de- 
liberate copy  of  the  shell — The  marvellous 
construction  and  fine  decoration  of  the  staircase — 
Why  it  is  left-handed — Its  date — Its  architect  was 
left-handed — Advantages  of  the  left-handed  forma- 
tion— The  double  spirals  of  Chambord  built  later 
— Creative  Imagination — The  Search  for  Beauty — 
The  Logarithmic  Spiral — The  foundations  of  Taste 
—  The  Ionic  volute  —  "  Majestati  Naturae  Par 
Ingenium" 164 


LIST    OF    ILLUSTRATIONS 


FIG.  PAGE 

Amboise,  from  a    Drawing  by    Leonardo    da   Vinci 

(photogravure)  ....      Frontispiece 

1.  Voluta  scalar  is    ......  1 

2.  Solarium  maximum        .  *  .  .  .7 

3.  Example  of  a  right-handed  and  of  a  left-handed  spiral        26 
4  The  "Prentice's  Pillar  "at  Rosslyn       .  .  .29 

5.  Narwhal's  tusks  .  .  .To  face  page     41 

6.  Elephant's  distorted  Tusk         .  .  „  41 

7.  Turbinella  pirum  .  .  .  .  .44 

8.  Turbinella  rapa  .  .  .  .  .  .44 

9.  Postage  Stamp  now  used  at  Travancore  .  .        45 

10.  Helicteres  ixora  (Seed-Pod)  .  .  '  .50 

11.  "  Lady's  Tresses  "  (Neottia  spiralis)        .          To  face  page  55 

12.  Pine  Cone           ......  54 

13.  Wax  Palm— Date  Palm              ....  56 

14.  Pandanus  utilis  ......  58 

15.  Case  made  by  larvae  of  Caddis-fly  (enlarged)    .            .  73 

16.  Capsule  of  Shark's  Egg .            ....  75 

17.  Bush-buck  shot  by    W.   Brodrick   Cloete  in  South 

Africa  ....  To  face  page     77 

18.  Tragelaphus  angasi  .  .  .  ,^77 

19.  Spiral  Twist :  A.  Angora— B.  Markhor  .  .         80 

20.  Spiral  Curve  ;  A.  Highland   Ram — B.  Merino   Ram 

0.    Alaskan    Bighorn    (Ovis    nivicola) — D.    Pamir 

Sheep— E.  Argali       .....  82 

21.  Spiral  Staircase,  Palazzo  Contarini,  Venice     To  face  page  95 

22.  Scalaria  scalaris  ......  95 

23.  Scala  del  Bovolo,  Palazzo  Contarini,  Venice  To  face  page  96 

24.  The  Tower  of  Pisa  ...  96 


XX 


LIST  OF   ILLUSTRATIONS 


FIG. 

25. 
26. 

27. 
28. 

29. 
30. 
31. 
32. 
33. 
34. 
35. 
36. 

37. 
38. 
39. 

40. 

41. 
42. 
43. 


44. 


45. 
46. 


47. 


Wing    of    the 


Escalier  de  la  Keine  Berthe,  Chartres 
Mitra  papalis 
Telescopium  telescopium  . 
Staircase    in    the    Old 

Blois  . 
Geritheum  giganteum 
Voluta  solandri    . 
Voluta  pacifica    . 
Turbinella  fusus  . 
Voluta  musica     . 
Nautilus  pompilius  (section) 
Logarithmic  Spiral 
Ammonites  (arielites)  obtusus, 

Lyme  Begis  . 
Argonauta  argo  . 
Operculum  of  Turbo  marmoratus 


PAGE 

To  face  page  97 

.    '     97 

98 

Castle    of 

To  face  page  98 

115 

119 

119 

120 

120 

To  face  page  123 

123 

From  the  Lower  Lias, 

To  face  page  124 
125 
124 


137 


Primitive  spiral  staircase,  with  plan  of  one  step 

Elaborate  spiral    staircase  with    plan    of    improved 

stonework       .  .  .  .  .  .142 

Two  floors  of  the  CMteau  of  Chambord,  showing  the 

interlacing  spirals  of  the  double  staircase   To  face  page  143 

Central  wooden  shaft  of  the  staircase  in  the  College 

de  Montaigu  .  .  .  .  .  .144 

Study  for  the  "  Leda,"  by  Leonardo  da  Vinci,  showing 
spiral  form  of  head-dress.  (From  the  IVindsor 
Collection)        ....  To  face  page  146 

Study  of  the  spirals  formed  by  smoke  and  dust.  By 
Leonardo  da  Vinci  (From  the  Windsor  Collec- 
tion)   .....  To  face  page  152 

Spiral  motion  of  the  tips  of  a  bird's  wings  „  154 

Professor  Marey's  photographs  of  a  flying  pigeon,  taken 
at  the  rate  of  fifty  a  second.  (From  Pearson's 
Magazine  for  May,  1902)       .  .  To  face  page  154 

A  page  of  Leonardo's  handwriting,  from  Leonardo's 
Manuscript  Note-book  on  the  Flight  of  Birds.  The 
transcription  of  Giovanni  Piumati  and  an  English 
version  of  the  translation  by  Charles  Ravaisson 
Mollien  ....  To  face  page  155 


LIST   OF   ILLUSTRATIONS  xxi 

FIG.  PAGE 

48.  Study  of  the  growth  of  flowers.     By  Leonardo  da 

Vinci.     (From  the  Windsor  Collection)         To  face  page  156 

49.  A.  and  B.     Study  of  the  spirals  formed  in  water.     By 

Leonardo  da  Vinci.      (From  the  Windsor  Collection) 

To  face  page    157 
50   Longitudinal  section  of  intestine  of  Raia  .  .159 

51.  Turritella  lentiginosa       .  .  .  .  .159 

52.  Auricula  auris-midm       .  .  .  .  .159 

53.  The  common  form  of  Voluta  vespertilio  (section)  .       165 

54.  Bare  form  of  Voluta  vespertilio  (section)  .  .165 

55.  Escalier  a  Jour,  Chateau   de  Blois,   Touraine.     The 

Central  Shaft             .            .  .          To  face  page  165 

56.  Common  form  of  Voluta  vespertilio  .             .             .166 

57.  Bare  form  of  Voluta  vespertilio  .  .            .            .166 

58.  Escalier  a  Jour,  Chateau  de  Blois,  Touraine.     The 

exterior  ....  To  face  page  166 

59.  Vaulting  and  steps  of  spiral  staircase  in  the  wing  of 

Francois  I.,  Chateau  de  Blois  .  To  face  page  170 

60.  A  and  B.    Left-handed  screws  from  Leonardo's  MSS. 

in  the  South  Kensington  Museum — C.  (From  the 
Windsor  Collection — D.  Signature  (from  the  Windsor 
Collection)       ....  To  face  page  175 

61.  Method  of  describing  the  Ionic  Volute  by  means  of  a 

common  whelk  shell. 

(1)  Shows  tape  entirely  wound  round  shell, 

and  pencil  in  position  to  start. 

(2)  Shows  tape  almost  unwound,  after  nearly 

completing  its  guidance  of  the  pencil. 

(3)  Capital  of  an  Ionic  Column. 

(4)  Chrysodomus  antiquus,   the  shell  used  to 

describe  the  volute  reproduced  To  face  page  188 


SPIRALS  IN   NATURE   AND 
ART 


•-•- ~"~~  •■'• 

L ......J!!,,  ^„,.^„;- «.,-  ■„* ** k. 


Giovanni  Bellini's  Allegory  of  the  Shell,  painted  for  the  owner  of  the  "Staircase  of  the 
Shell,"  in  the  Palazzo  Contarini,  Venice  {see  page  95). 

[To  face  page  1. 


CHAPTER  I 


THE   ARGUMENT 


"  Ihr  durchstudiert  die  gross'  und  kleine  "Welt 
Um  es  am  Ende  gehn  zu  lassen 
Wie's  Gott  gefallt. 

Vergebens,  dass  ihr  ringsum  wissenchaftlich  schweift 
Ein  jeder  lernt  nur,  was  er  lernen  kann." x — Mephistopheles. 

"  II  pittore  deve  essere  universale." — Leon,  da  Vinci. 

KOR  the  existence  of  an  Essay 
upon  Spiral  Formations  in 
Nature  and  Art,  no  better 
apology  can  be  offered 
than  the  interest  and  beauty 
of  an  inquiry  which  has 
hitherto  only  been  sug- 
gested in  a  few  scattered 
Fig.  i.  pamphlets    and    disconnected 

valuta  scaiaris.        references.      But    an    excuse 
is    certainly    needed    for   the    fact    that    this 

1  "  "Pis  best  to  study  all  things — everywhere — 
Nature  and  man — the  great  world  and  the  small, 
Then  leave  them  at  haphazard  still  to  fare, 
It  is,  you  see,  plainly  impossible 
That  one  man  should  be  skilled  in  every  science, 
Who  learns  the  little  that  he  can  does  well." 
{From  Goethe  s  Faustus. 
Translated  by  John  Anster.) 
A  X 


2  THE  ARGUMENT  [chap. 

inquiry  was  undertaken  by  one  who  knew 
little  history,  less  architecture,  scarcely  any 
mathematics,  and  no  morphology  or  botany 
whatever.  A  deep  knowledge  of  all  five 
seemed  indispensable.  But  as  the  most 
profound  acquaintance  with  only  one,  or 
even  only  two,  was  useless,  I  have  ventured, 
perhaps  too  boldly,  to  believe  that  to  have 
specialised  in  none,  and  to  have  the  keenest 
sympathy  with  each,  is  as  good  a  qualification 
for  the  task  as  may,  for  the  moment,  be 
attained.  My  belief  is  all  the  easier  because 
it  is  accompanied  by  the  confidence  that  every 
specialist  will  delightedly  correct  those  errors 
which  occur  in  ground  familiar  to  him,  while 
he  may  perhaps  be  tempted — by  their  mere 
proximity — to  consider  questions  which  he  has 
hitherto  too  often  set  aside  as  being  beyond 
his  special  province. 

In  either  case  I  shall  be  sufficiently  rewarded. 
But  I  would  not  have  it  thought  that  I  have 
approached  these  matters  lightly  or  suddenly. 
They  have  been  constantly  in  my  mind  for 
thirteen  years,  and  if  I  at  length  presume  to 
offer  the  result  of  my  endeavours  to  the 
public,  it  is  because  many  of  the  questions 
to  which  an  intelligible  reply  is  sought  have 
not  yet  been  answered  in  any  of  the  five 
divisions  of  intellectual  research  already 
mentioned,    though    distinguished    exponents 


i.]  THE   SPECIALIST  3 

of  each  are  firmly  convinced  that  a  reply 
might  be  furnished  by  the  others.  It  is  in 
the  hope  of  eliciting  such  replies  that  these 
tentative  pages  have  been  published.  To 
remain  silent  for  lack  of  perfect  detail  in  each 
part,  were  but  to  strengthen  the  negative 
gloom  of  the  narrow  specialist,  whose  motto 
might  well  be  the  warning  placed  at  the  head 
of  this  chapter,  the  lines  that  were  spoken  by 
"  The  Spirit  who  Denies." 

I  do  not  give  the  names  of  many  who  have 
offered  me  the  kindest  and  most  generous 
assistance.1  They  are  all  aware  of  my 
gratitude ;  and  none  of  them  might  wish 
to  be  made  even  remotely  responsible  for 
suggestive  generalisations  that  are  unfettered 
by  too  keen  an  appreciation  of  difficulties 
in  detail.  Though  I  have  been  at  great  pains 
to  verify  the  facts  here  recorded,  I  will  there- 
fore beg  that  the  architect  will  particularly 
scrutinise     my     biological     statements ;     the 

1  To  helpers  of  a  different  kind  I  must  express  my 
thanks  by  name,  for  without  the  careful  drawings  made 
by  Mr  T.  Green  of  Wallington,  and  the  no  less  skilful 
wood  engravings  of  Mr  Butterworth  of  Savoy  House,  my 
argument  would  have  entirely  lost  some  of  the  most 
convincing  of  its  aids.  The  design  of  the  twining  hop-plant 
on  the  binding,  and  the  drawing  of  "  Lady's  Tresses  "  in 
the  text,  are  my  mother's  work.  Messrs  Sowerby  and 
Fulton  of  Kew  have  been  of  great  assistance  in  choosing 
some  specimens  of  shells  for  me. 


4  THE  ARGUMENT  [chap. 

mathematician  my  excursions  into  art;  and 
that  the  historian  will  look  indulgently  upon 
one  result  which  seems  to  flow  from 
arguments  based  alternately  upon  both — a 
result  which,  in  the  absence  of  all  documents, 
does  not  admit  of  perfect  proof. 

With  this  modest  study  in  spiral  formations 
the  great  name  of  Leonardo  da  Vinci  has 
been  connected  on  my  title-page  for  reasons 
that  will  soon  become  evident.  But  the 
incident  that  first  associated  the  two  in  my 
own  mind  deserves  recording,  both  as  an 
explanation  of  these  pages  and  as  an  example 
of  scientific  insight. 

Just  thirteen  years  ago  I  was  dining  at 
Oxford,  in  company  with  some  distinguished 
biologists.  Each  seemed  to  have  something 
of  value  either  to  relate  or  to  display,  and  the 
unlearned  guest  was  feeling  a  little  at  a  loss  for 
any  topic  of  discourse  in  a  conversation  which 
ranged  so  far  beyond  his  own  experience  and 
knowledge.  At  length  he  ventured  to 
produce  for  general  inspection  a  proof  engrav- 
ing upon  Indian  paper  of  a  certain  staircase 
(see  fig.  59),  built  by  an  architect  whose  name 
has  been  hitherto  unknown  in  the  early 
sixteenth  century  at  Blois.  I  had  but  just 
returned  to  Oxford  after  a  long  visit  to  the 
banks  of  the  Loire.  I  had  endeavoured  to 
investigate  the  historical  and  artistic  associa- 


l]  A   DISCOVERY  5 

tions  of  that  wonderful  valley  for  a  book,1  to 
whose  publishers  I  felt  deeply  indebted  for 
thus  bringing  into  greater  prominence  a 
miracle  of  design  which  now  seemed  to 
promise  even  greater  fascinations  than  those 
discovered  in  it  already. 

The  little  picture  was  indulgently  received ; 
and  the  joy  of  its  humble  possessor  may  be 
imagined  when  one  of  the  party  loudly 
proclaimed  his  recognition  of  the  spiral  curve 
therein  depicted.  No  sympathy  was 
suggested  with  any  architectural  problem; 
but  the  critic  who  now  held  the  picture  of 
the  spiral  staircase  in  his  hand  announced  to 
his  comrades  that  the  curves  upon  its  central 
column  were  identical  with  those  of  Voluta 
vespertilio  (see  fig.  56). 

Abashed,  befogged,  but  keenly  interested, 
I  hinted  at  my  ignorance  of  what  Voluta 
might  be.  The  shell  was  fetched.  Still  I 
remained  unmoved  and  unilluminated. 
Finally  the  Professor  had  pity  upon  me.  A 
longitudinal  incision  was  made,  and  the  four- 
fold spiral  stood  revealed  within  upon  the 
columella  (see  fig.  53). 

Every    one    was     soon     talking    of    other 

subjects,  but  I  could   think   of  nothing   else. 

In  spite   of  many  other  conflicting   interests 

and   duties    I   have   thought   of  that    chance 

1  "Old  Touraine"  (Bivingtons,  1892). 


6  THE   ARGUMENT  [chap. 

discovery  ever  since.  If  a  biologist  could 
recognise  the  lines  that  are  hidden  within  a 
certain  shell  as  soon  as  he  saw  them  repro- 
duced in  a  French  staircase,  there  was  also 
the  possibility  that  the  staircase  had  been 
originally  suggested  by  the  shell.  This  idea 
turned  my  thoughts  to  other  spiral  staircases 
and  other  shells.  I  found  that  a  Scala  della 
conchiglia  and  a  Scala  del  bovolo  (fig.  21) 
were  to  be  seen  in  Italy ;  and  that  in  the 
Natural  History  Museum  at  South  Kensington 
there  were  a  Voluta  scalaris  (fig.  1),  a  Solarium 
maximum  (fig.  2),  even  a  Scalaria  scalaris 
(fig.  22).  The  connection  between  shells  and 
staircases  was  evidently  present  in  the  minds 
both  of  those  scientists  who  had  bestowed 
these  names  on  shells,1  and  of  those  persons 
who  had  seen  and  admired  a  building 
sufficiently  to  recognise  the  natural  objects 
it  recalled.  This  by  no  means  involved  that 
certain  architectural  forms  could  be  explained 
on  a  conchological  basis,  or  that  conchology 
should  ever  be  considered  from  an  architec- 
tural point  of  view.  But  it  certainly  did 
suggest    that    a    staircase    whose    form    and 

1  The  name  Voluta  was  given  by  Linnaeus.  The  species 
Scalaris  was  described  and  named  from  the  Barton  Beds 
(Middle  Eocene)  by  J.  de  C.  Sowerby  in  1843.  It  may 
be  noted  that  fossils  in  these  beds  are  wonderfully 
preserved,  even  in  colour,  and  include  a  very  large 
number  of  columellar  spirals. 


I.] 


NAMES  OF  SHELLS 


7 


construction  recalled  a  natural  growth  would 
more  probably  be  the  work  of  a  man  to  whom 


Fig.  2. 

Solarium  maximum, 


biology  and  architecture  were  equally  familiar 
than  that  of  a  builder  of  less  wide  attainments. 
It  would,  in  fact,  be  likely  that  the  design  had 


8  THE  ARGUMENT  [chap. 

come  from  some  great  artist  and  architect 
who  had  studied  Nature  for  the  sake  of  his 
art,  and  had  deeply  investigated  the  secrets 
of  the  one  in  order  to  employ  them  as  the 
principles  of  the  other. 

It  seems  difficult  for  many  architects, 
when  they  commit  their  thoughts  to  paper, 
to  express  their  views  moderately,  so  deep 
are  their  personal  convictions  of  what  is  right 
and  wrong.  Some  critics  objected  so  vehe- 
mently to  one  portion  of  these  pages  in  their 
earliest  form *  that  they  apparently  refused  to 
consider  any  other. 

As  a  matter  of  fact,  I  most  thoroughly 
accept  the  commonplace,  that  Art  is  one  thing, 
and  Nature  is  another,2  and  that  mere  un- 
intelligent copying  of  natural  phenomena 
will  never  be  artistic,  however  faithfully 
performed.  Structural  forms  in  architecture 
— it  is  as  great  a  platitude  as  the  other — are 
usually  the  result  of  direct  problems  in 
building.  Yet  I  do  not  hesitate  to  say  that 
the  philosophy  of  Architecture  must  finally 
be  based  on  general  principles  which  will 
appeal  to   other  intelligences    than   those   of 

1  In  The  Monthly  Review  for  April  and  May  1902. 

2  "Nature,"  wrote  Whistler,  " contains  the  elements,  in 
colour  and  form,  of  all  pictures,  as  the  keyboard  contains 
the  notes  of  the  piano,"  but,  "  to  say  to  the  painter  that 
Nature  is  to  be  taken  as  she  is,  is  to  say  to  the  player  that 
he  may  sit  on  the  piano." 


L]  MATHEMATICS  9 

the  strictly  professional  architect.  On  the 
other  hand,  though  natural  forms,  unmodified 
and  unrestrained,  can  never  become  architec- 
tural ornaments,  yet  it  is  not  necessary  to  lose 
all  the  charms  of  natural  beauty  by  exaggerated 
convention,  or  by  too  rigid  application  of  the 
square  and  the  ruler.  Indeed,  I  shall  show 
in  later  pages  that  it  is  only  by  appreciating 
the  irregularities  of  Nature  that  beauty  can 
ever  be  artificially  attained  (see  p.  185). 

Language  is  not  literature ;  nor  is  mere 
verse  poetry.  Style  is  not  attained  by  over- 
elaborated  exactness,  nor  is  industrious 
reproduction  an  attribute  of  genius.  Architec- 
ture should  take  her  right  place  at  the  head  of 
all  the  Arts,  because  she  can  most  clearly 
manifest  that  divine  attribute  in  man  which 
is  connoted  in  Creation;  and  the  creative 
imagination  is  no  more  concerned  with  fancies 
only  than  it  is  with  facts  alone ;  it  deals  with 
the  material  of  scientific  knowledge,  and  with 
the  causes  that  underlie  phenomena,  in  order 
to  evolve  new  combinations  of  its  own. 

No  one  has  yet  been  able  to  say  who 
designed  the  open  staircase  in  the  wing  of 
Francois  I.  at  Blois,  which  is  reproduced  in 
figs.  55,  58,  and  59.  If  it  were  really  the 
conscious  copy  of  a  shell,  the  first  step 
towards  a  discovery  of  its  designer  would 
be  to  find  a  man  who  lived  near  Blois  between 


10  THE  ARGUMENT  [chap. 

1515  and  1520,  who  was  a  friend  of  Francois 
L,  who  was  something  more  than  a  mere 
master-mason,  and  who  was  likely  to  have 
studied  shells  not  merely  as  a  biologist,  not 
merely  as  an  artist,  but  also  as  a  scientist 
and  a  philosopher,  who  was  in  search  of  those 
hidden  natural  causes  which  might  be  applied 
to  the  products  of  human  handiwork.  To 
all  these  somewhat  general  qualifications  there 
is  but  one  man  who  can  justly  lay  claim — 
Leonardo  da  Vinci,  that  great  Italian  artist, 
mathematician,  scientist,  and  engineer,  who 
died  in  exile  within  a  few  miles  of  this  very 
staircase  a  year  or  two  after  it  had  been 
begun. 

The  main  impression  produced  by  this 
building  is  its  spiral  formation.  It  is  there- 
fore likely  that  its  builder  would  have  given 
particular  attention  to  spiral  formations  in 
Nature,  with  the  object  of  discovering  the 
principles  involved  in  them.  I  shall  hope 
to  show  that  this  was  one  of  the  many 
problems  to  which  Leonardo  turned  his  extra- 
ordinarily original  and  acquisitive  intellect ; 
and  in  the  various  instances  of  natural  spirals 
which  I  have  collected  I  would  also  point 
out  that  the  original  indication  was  given 
me,  in  almost  every  case,  in  his  manuscript 
notes.  These  manuscripts  suggest  many 
problems   which   even  the   present   advanced 


i.]  LEONARDO'S  MANUSCRIPTS  11 

state  of  scientific  knowledge  is  unable  as  yet 
to  answer;  and  therefore  my  original  voyage 
of  discovery  in  search  of  the  designer  of  a 
particular  staircase  has  led  me,  by  natural  and 
unavoidable  paths,  into  an  inquiry  which 
ranges  far  beyond  either  the  building  or  its 
builder,  and  leads  towards  those  ultimate 
principles  of  construction  and  of  growth  which 
Leonardo  did  so  much  to  discover,  and  which 
his  successors  are  still  endeavouring  to  grasp. 
Though  less  than  a  dozen  undisputed  examples 
of  Leonardo's  paintings  exist,  it  is  chiefly 
as  a  painter  that  he  is  known  to  general 
fame.  The  bulk  of  his  sketches  and  manu- 
scripts in  this  country  exceeds  by  many  times 
the  whole  of  those  possessed  by  other  nations, 
yet  the  value  and  contents  of  these  do  not 
seem  to  be  so  well  appreciated  in  England 
as  they  are  elsewhere.  They  have  been 
investigated  by  Venturi,  Libri,  Govi,  Kichter, 
Ravaisson-Mollien,  Beltrami,  Miintz,  Miiller- 
Walde,  Uzielli,  Sabachnikoff  (fig.  47),  Piumati, 
Duval,  Seailles,  and  the  editors  of  the  facsimile 
edition  of  the  Milan  manuscripts,  to  name  no 
more.  Apart  from  the  actual  drawings  and 
studies  they  contain,  these  manuscripts  are  very 
much  like  the  notes  that  might  be  made  by  an 
exceptional  Professor  for  a  course  of  very  extra- 
ordinary lectures.  They  display  a  gift  of  literary 
expression  and  construction  which   lags   very 


12  THE   ARGUMENT  [chap. 

far  behind  the  ardour  for  discovery  that  in- 
spired them.  For  this  reason  their  writer 
remained  almost  unheard  by  his  con- 
temporaries, and  is  scarcely  yet  appreciated 
by  his  posterity.  His  arguments  are  not 
presented  in  that  logical  form  which  helps  a 
reader  to  understand  their  drift.  His  discus- 
sion of  the  connection  between  the  Scriptural 
Deluge  and  the  fossil  shells  found  upon  a 
mountain-top  is  one  of  the  few  cases  in  which 
the  literary  form  of  the  inquiry  is  complete. 
It  is  therefore  only  natural  that  the  isolation 
of  his  own  intellectual  life  should  have  been 
almost  reproduced  in  the  comparative  neglect 
of  his  manuscripts  in  later  years.  It  was  one 
of  his  favourite  sayings  that  the  strength  of 
the  painter  was  in  solitude  : — "  Se  tu  sarai 
solo,  tu  sarai  tutto  tuo." 

Another  drawback  is  the  material  one  of  the 
difficulty  in  deciphering  his  writing.  Whether 
it  be  true  or  not  that  it  was  owing  to  travels  in 
the  East  that  he  took  to  writing  from  right 
to  left,  it  is  certain  that  he  largely  employed 
a  caligraphy  which  can  best  be  read  in  a 
mirror  (see  fig.  47),  and  which  was  also  an 
easy  accomplishment  for  a  left-handed  man.1 

1  A  landscape  drawing  in  the  Uffizi — the  authenticity  of 
which  has  never  been  called  in  question— is  dated  "  The 
day  of  S.  Mary  of  the  Snow,  the  5th  day  of  August,  1473," 
when  Leonardo  was  just  twenty-one  ;  and  Mr  M 'Curdy  has 


L]  LEFT-HANDED  13 

If  the  shading  of  his  drawings  had  not 
revealed  the  peculiarity,  we  should  have  known 
that  Leonardo  was  left-handed  from  the 
statement  of  his  friend  Fra  Luca  Pacioli,  for 
whose  book,  "De  Divina  Proportioned'  he 
designed  the  figures. 

These  are  some  of  the  reasons  why  the 
secrets  of  a  man  who  spent  the  last  years  of 
his  life  in  exile  at  the  beginning  of  the 
sixteenth  century  remained  his  own  until 
the  last  years  of  the  nineteenth.  Yet  his 
fame  is  only  strengthened  by  that  long 
oblivion.  For  the  laws  which  he  established 
or  divined  have  been  independently  discovered 
and  proved  as  advancing  knowledge  made 
researches  easier ;  and  the  reputation  of  his 
successors  remains  untarnished ;  for  though 
their  discoveries  must  now  be  antedated  by 
three  or  four  centuries,  they  made  them  in 
their  turn  while  Leonardo's  manuscripts  were 
still  unknown.  A  sower  of  ideas  of  which 
he  never  saw  the  harvest,  he  jealously  guarded 
them  from  intrusion  during  his  lifetime,  and 
they  never  came  to  light  till  long  after  his 
death. 

pointed  out  that  this  inscription  shows  Leonardo  had 
already  adopted  the  method  of  writing  from  right  to  left ; 
so  that  I  prefer  the  theory  that  this  was  the  natural  method 
of  the  left-handed  man,  rather  than  the  acquired  result  of 
any  possible  travels  in  the  East, 


14  THE  ARGUMENT  [chap. 

Before  me  as  I  write  are  some  five  hundred 
careful  photographs  of  the  originals  existing  in 
England,  to  which  it  may  be  hoped  that  a  fuller 
justice  will  some  day  be  done  than  I  can  now 
find  to  be  the  case.  Though  it  was  necessary 
to  examine  all  of  them,  only  a  very  small 
fraction  bore  upon  the  special  subject  of  this 
work,  and  only  a  very  few  examples  have  been 
chosen  out  of  these  to  indicate  the  kind  of 
material  available  (see  figs.  43,  44,  47,  49),  and 
to  produce  the  barest  essentials  in  the  progress 
of  this  argument.1  They  embrace  drawings  of 
landscape  and  figures,  which  are  evidently 
studies  for  pictures ;  anatomical  drawings  of 
great  beauty  and  skill ;  botanical  sketches, 
architectural  plans,  biological  notes,  numerous 
engineering  problems,  many  mathematical 
inquiries,  the  whole  dashed  down  without  much 
order,  in  a  very  fervour  of  investigation.2 

Carrying   as   he   did,   in   that   brain   which 

1  I  have  also  examined  the  MSS.  in  Paris,  Venice, 
and  Milan,  where  the  numbering  of  the  great  "Codice 
Atlantico"  has  been  corrected  by  the  Abb6  Ceriani,  and 
the  whole  is  being  reproduced  at  the  cost  of  the  State. 

2  Though  many  pages  that  have  survived  cannot,  under 
any  hypothesis,  be  considered  as  prepared  for  publication, 
there  is  some  evidence  in  others  that  Leonardo  not  only 
wrote  for  a  public,  but  was  conscious  of  his  literary  short- 
comings. "Blame  me  not,  0  reader,"  he  says,  for  instance, 
in  one  note-book,  "for  the  subjects  are  numberless,  and 
my  memory  is  weak,  and  I  write  at  long  intervals.  ..." 


L]  RESEARCH  15 

bore  so  many  images  of  beauty,  not  only  all 
the  science  known  at  the  beginning  of  the 
sixteenth  century,  but  almost  half  of  the 
attainments  that  the  years  since  then  have 
brought  us,  Leonardo  lived  of  necessity  a 
lonely  life ;  and  with  advancing  years  it  is 
known  that  his  thoughts  turned  more  and  more 
from  painting  to  problems  of  natural  science, 
and  to  vast  collections  of  natural  objects.  His 
quest  was  that  of  Goethe's  Faust : — 

"  Das  ich  erkenne,  was  die  Welt 
Im  innersten  zusammenhalt 
Schau'  alle  Wirkenskraft  und  Samen 
Und  thu  nicht  mehr  in  Worten  Kramen."  x 

It  was  a  characteristic  of  his  genius  that 
the  patent  phenomena  of  life  did  not  content 
him.  He  insisted  on  going  deeper.  "Ma 
tu  che  vivi  di  sogni"  he  writes  in  the 
Treatise  on  Flying  (fig.  47),  "  ti  piace  pin  le 
ragion  soffistiche  e  barerie  de  palari  nelle  cose 
grande  e  incerte,  che  delle  certe,  naturali,  e 
non  di  tanti  altura" 2     His  intellect  was  as 

1  "  0  for  a  glance  into  the  earth  ! 
To  see  below  its  dark  foundations 
Life's  embryo  seeds  before  their  birth.  ..." 
(Goethe  s  Faustus,  trans,  by  John  Anster.) 
2  "But  thou  who   livest  in   dreams  art  more  pleased 
even  with    the    sophistical    reasonings    and    theories    of 
philanderers,  when  they  deal  with  great  and  unknown  matters, 
than  with  researches   into  things   certain,   natural,    and 
of  a  lower  interest." 


16  THE  ARGUMENT  [chap. 

sincere  as  it  was  sagacious.  He  penetrated 
the  secret  hiding-places  of  truth  with  a 
passionate  industry  that  never  shrank  from 
toil.  "  Truth/'  he  cries,1  "  is  so  excellent  that 
by  her  praise  the  very  smallest  things  attain 
nobility."  His  method  was  that  of  Darwin, 
proceeding  by  an  analysis  which  does  not 
fear  to  be  diffuse;  grouping  isolated  pieces 
of  evidence,  attaining  at  last  a  final  law,  or 
at  least  a  hypothesis  that  would  explain  the 
facts.  His  anatomical  drawings,  apart  from 
their  exquisite  draughtsmanship,  contain  so 
many  keen  parallels  and  suggestive  indica- 
tions that  the  author  of  the  "  Origin  of 
Species"  would  have  perused  them  with 
delight.2  It  is  perhaps  a  loss  both  to  Science 
and  to  Art  that  the  majority  of  Leonardo's 
manuscripts  do  not  seem  to  have  been  known, 
as  far  as  we  are  aware,  either  to  Darwin  or  to 
Ruskin. 

I   shall   have   occasion   to  mention   several 
instances   of  Leonardo's   use   of  that  experi- 

1  The  passage  begins  as  follows:  "Ed  5  di  tanto 
vilipendio  la  bugia,  che  s'ella  dicessi  be'gran  cose  di  dio, 
ella  to'  di  grazia  a  sua  deit& ;  ed  6  di  tanta  eccellenzia  la 
veritk  .  .  ." 

2  In  the  manuscripts  at  Windsor,  for  example,  there  are 
careful  drawings  to  show  that  the  tail  in  other  animals 
existed  in  a  modified  form  in  man.  Huxley's  manuscript 
memoranda  are,  I  am  informed,  full  of  delicate  drawings, 
and  in  other  ways  somewhat  similar  to  those  of  Leonardo, 


ij  IMAGINATION  VI 

mental  method  which  Humboldt  recom- 
mended and  Galileo  used.  He  understood 
to  the  full  the  definition  of  Science  as  "the 

knowledge     of    Causes  "—Tore    eirurrd[i€0a    6W    rrjv 

airlav  ctSw/Acv.  He  realised  even  more  keenly  the 
necessity  that  Science  should  be  largely  oc- 
cupied with  speculations,  with  hypotheses, 
with  imaginations,  with  what  Miiller  in  1834 
called  "  Phantasie." 1  Nature  must  be  inter- 
rogated in  such  a  manner  that  the  answer 
is  implicit  in  the  question.  The  observer  can 
only  observe  when  his  search  is  guided  by 
the  thread  of  a  hypothesis.  It  is  the  thread 
of  spiral  formations  that  has  guided  these 
chapters.  It  was  the  manuscripts  of  Leon- 
ardo which  inspired  them. 

The  laborious  collection  of  facts  alone  is 
powerless  if  it  does  not  go  further.  The 
imagination,  unrestricted,  can  neither  con- 
vince  nor   gratify.     But   in   combination   the 

1  "Die  Phantasie  ist  ein  unentbehrliches  Gut;  denn  sie 
ist  es,  durch  welche  neue  Combinationen  zur  Veranlassung 
wichtiger  Entdeckungen  gemacht  werden.  Die  Kraft  der 
Unterscheidung  des  isolirenden  Verstandes,  sowohl  als  die 
der  erweiternden  und  zum  Allgemeinen  strebenden  Phan- 
tasie sind  dem  Naturforscher  in  einem  harmonischen 
Wechselwirken  nothwendig.  Durch  Storung  dieses  Gleich- 
gewichts  wird  der  Naturforscher  von  der  Phantasie  zu 
Traumereien  hingerissen,  wahrend  diese  Gabe  den  talent- 
vollen  Naturforscher  von  hinreichender  Verstandesstarke 
zu  den  wichtigsten  Entdeckungen  fiihrt." — Joh.  Muller, 
Arch,  fur  Anat.  1834. 

B 


18  THE  ARGUMENT  [chap. 

two  can  do  what,  for  w^ant  of  a  better  word, 
we  call  "  create." 

This  was  Leonardo's  meaning  when  he  said 
that  "  the  works  of  Nature  are  finite."  They 
move  along  those  orderly,  those  vast,  processes 
of  time  and  space  which  can  be  realised  by 
that  human  intelligence  which  is  a  part  of 
them,  if  only  it  will  work  hard  enough  to 
collect  the  details. 

"  Ich  stand  am  Thor ;  ihr  solltet  schliissel  sein  ; 
Zwar  euer  Bart  ist  kraus,  doch  hebt  ihr  nicht  die  Riegel. 

Geheimnissvoll  am  lichten  Tag 
Lasst  sich  Natur  des  Schleiers  nicht  berauben 
Und  was  sie  deinem  Geist  nicht  offenbaren  mag, 
Das  zwingst    du    ihr  nicht    ab   mit  Hebeln   und  mit 
Schrauben." 1 

This,  then,  is  to  "  know  "  ;  but  to  "  create  " 
is  greater,  for  creation  takes  that  further  step 
which  is  beyond  knowledge,  yet  must  ever 
be  based  on  knowledge ;  and  this  is  the  truth 
which  the  great  Italian  expressed  in  that  hard 
saying  of  the  eye  surpassing  Nature ;  for  he 
realised  that  "  the  things  which  eye  and  hand 

1  "  I  stand  before  the  guarded  door 
Of  Nature,  but  it  bids  defiance 
To  latch  or  ward  :  in  vain  I  prove 
Your  powers — the  strong  bolts  will  not  move. 
Mysterious  in  the  blaze  of  day- 
Nature  pursues  her  tranquil  way.  .  .  ." 

(Goethe's  Faustus,  trans,  by  John  Anster.) 


i.]  THE  ITALIAN  FAUST  19 

can  create  are  infinite."  "AH  things  are 
artificial/'  said  Sir  Thomas  Browne,  "for 
Nature  is  the  art  of  God." 

Michelet    described    Leonardo,   in    a    tho- 
roughly characteristic  phrase,  as  "the  Italian 
brother  of  Faust "  ;  but  there  is  an  even  closer 
parallel  between  the  Italian  and  Faust's  great 
creator,    Goethe.       For    the    genius    of    the 
German  shone  not  merely  in  the  poetry  and 
prose  of  which  he  is  the  acknowledged  master, 
but  in  osteology,  in  botany,  in  morphology, 
in  anatomy,  in  optics,  in  the  theory  of  archi- 
tecture.    His  name  will  indeed  be  connected 
with  some  of  these  as  long  as  it  is  honoured 
in    the     language     he     immortalised.       Like 
Leonardo,  Goethe  projected  a  mind  that  was 
primarily    artistic    into     all     those     scientific 
problems  which  the   errors  or   inadequacy  ot 
his  time  had  left  incomplete.     Such  prophetic 
insight  as  was  theirs  is  never  understood   in 
the   age   of  which   it   is   a  part.     But  when 
their  day  has  itself  become  a  portion  of  the 
past,  then  their  own  value  emerges  clear,  in 
its   true   perspective,  above  the  many-headed 
ignorance  that  once  shrouded  them ;  for  "it  is 
not  the  intelligent  man,  but  Intelligence,  that 
rules."      "There    is    no    such    thing,"    cried 
Goethe,   "as    a  patriotic  art."      Like   all  else 
that   is   great   and   good   and  true,   Art   and 
Science   belong   to    the   whole   world.     It    is 


20  THE  ARGUMENT  [chap. 

only  by  constant  reference  to  our  great  in- 
heritance, and  by  a  constant  interchange 
of  ideas  between  every  contemporary  worker, 
that  we  can  advance  at  all.  This,  therefore, 
is  another  reason  why  I  have  ventured  to 
ask  the  architect  to  consider  the  biologist 
in  a  kindlier  light,  and  invited  the  mathe- 
matician and  the  botanist  to  lie  down  together. 
It  is  only  by  such  intercommunication  as 
modern  inventions  and  modern  tolerance 
have  rendered  possible  that  any  of  us  can 
ever  approach  that  large  point  of  view  which, 
in  the  case  of  Leonardo,  was  possible  to  a 
single  man.  " La  Nature"  said  Rodin,  " cest 
le  rnodele  variable  et  infini  qui  contient  tous 
les  styles.  JElle  nous  entoure,  mais  nous  ne 
la  voyons  pas"  The  ideal  of  the  sculptor 
speaking  at  the  dawn  of  the  twentieth  century 
was  that  of  the  artist  working  in  the  fifteenth. 
As  has  been  finely  said  of  the  Frenchman, 
he  knew  "all  there  is  to  know  of  the  apti- 
tude of  clay  to  receive,  of  marble  to  declare, 
his  own  intimate  interpretation  of  those  large 
secrets  of  the  Universe  which  escape  the 
narrow  definitions  of  logic  and  of  language/'1 
But  Leonardo  went  further  than  this ;  for 
he  possessed  to  an  extraordinary  degree  that 
masterful  quality  of  the  human  mind  which 
Goethe  called  "  das  Damonische,"  that  power 
1  Rt.  Hon.  George  Wyndham,  15th  May  1902. 


i.]  SCIENTIFIC  WORK  21 

which  makes  and  transforms  ideas,  that  living 
and  constructive  energy  which  flings  itself  into 
the  future  wrhile  it  assimilates  the  present. 

"  Ich,  mehr  als  Cherub,  dessen  freie  Kraft 
Schon  (lurch  die  Adern  der  Natur  zu  fliessen.  .  .  ."  1 

It  must  be  remembered,  too,  that  Leonardo 
lived  and  laboured  in  an  age  when  what  we 
may  call  "the  scientific  sense"  was  far  less 
developed  than  it  is  now,  and  when  the 
multitudinous  possibilities  of  the  printing 
press,  the  camera,  and  the  telegraph  were 
either  unknown  or  unappreciated.  In  his 
library,  biology  was  represented  by  Pliny, 
John  de  Manderville,  and  "a  lapidarium." 
Yet  he  suggested  the  theory  of  the  eye, 
which  was  slowly  elaborated  from  Leonardo 
to  Kepler,  from  Kepler  to  Helmholtz. 

"  II  Moto,"  he  wrote,  "  e  causa  d'ogni  vita." 
"Activity,"  said  Professor  Clifford  four 
hundred  years  afterwards,  "is  the  first  con- 
dition of  development."  Leonardo  was  the 
first  to  propose  a  division  of  animals  into 
vertebrates  and  invertebrates.  He  guessed 
that  the  blood  circulated,  but  could  not 
explain   the   mechanism.       "The    heart,"    he 

1  "High  above  cherubs — above  all  that  serve 
Raised  up  immeasurably — every  nerve 
Of  Nature's  life  seemed  animate  with  mine.  .  .  .' 
(Goethe's  Faustus,  trans,  by  John  Anster.) 


22  THE  ARGUMENT  [chap. 

wrote,  "is  a  muscle  of  great  strength  .  .  . 
the  blood  which  returns  when  the  heart 
opens  again  is  not  the  same  as  that  which 
closes  the  valves." 

Long  before  Bernard  Palissy  he  studied  the 
fossil  shells  on  mountain  tops,  and  showed 
that  "the  Deluge  had  nothing  to  do  with 
them,"  and  that  they  were  remains  of  living 
organisms,  left  there  by  water,  "Nature's 
Charioteer,"  in  the  course  of  prolonged 
changes  in  the  surface  of  the  earth,  and 
revealing  in  their  fossil  state  the  circum- 
stances of  their  far-off  existence.  He  thought 
that  "the  sandy  desert  beyond  Mount 
Atlas"  had  formerly  been  "covered  with 
water,"  and  anticipated  Cuvier  by  showing 
that  the  level  of  the  sea's  bottom  is  con- 
tinually rising,  sometimes  rapidly,  sometimes 
by  lengthy  accumulations  of  debris,  and 
pointed  out  the  strata  in  the  stone  of  the 
Apennines  revealed  by  the  cutting  of  the 
river  Lamona.  He  gave  as  long  as  two 
hundred  thousand  years  for  the  accumula- 
tions formed  by  the  river  Po ;  and  in  geology 
his  investigations  directly  foreshadow  in  other 
ways  the  work  of  Lyell,  who  established 
geology  as  a  science  by  showing  that  the 
causes  which  had  produced  the  past  were 
still  at  work  producing  the  future,  just  as 
Darwin   not   only   explained    the   biology   of 


l]  PHYSICAL  DISCOVERIES  23 

vanished  forms,  but  gave  the  reasons  for 
further  development,  and  assigned  living 
things  to  their  right  place  in  the  great  order 
of  Nature. 

Besides  founding  the  study  of  anatomy 
Leonardo  was  the  first  to  investigate  the 
structural  classification  of  plants,  and  (in  the 
fourth  book  of  the  "  Trattato  "  )  to  study  the 
system  on  which  leaves  are  disposed  and 
arranged  about  their  stalks,  and  laid  down 
laws  which  were  re-discovered  independently 
in  the  seventeenth  century.  He  explained  the 
suspension  of  bodies  in  the  air,  and 
experimented  on  the  consistency  of  the 
atmosphere  at  various  heights,  besides  going 
far  towards  a  solution  of  those  problems  of 
flying  which  still  occupy  us  to-day.  "  II  sole 
non  si  move/'  he  wrote,  anticipating 
Copernicus  in  propounding  his  theory  of 
the  movement  of  the  earth  round  the  sun, 
and  explaining  to  the  dogmatists  of  his  day 
that  "  the  supreme,  wisdom  of  God 1  guided 
him  to  choose  those  laws  of  movement  which 
were  in  closest  agreement  with  abstract 
and  metaphysical  reasoning." 

He  laid  the  foundations  for  those  laws 
of  the  movement   and   equilibrium   of  fluids 

1  Compare  the  "  Digression  of  the  Wisdom  of  God  in  the 
Site  and  Motion  of  the  Sun "  in  Sir  Thomas  Browne's 
"  Vulgar  Errors,"  VI.  v. 


24  THE  ARGUMENT  [chap. 

which  were  completed  by  Pascal,  D'Alembert, 
Bernouilli,  and  others.  He  proved  that  water 
in  communicating  vessels  remained  at  the  same 
height  in  each,  which  was  the  theory  of  the 
hydraulic  press  of  1653.  Attracted  irresistibly 
by  the  practical  problems  of  the  Scriptural 
"  Deluge/5  he  covered  innumerable  sheets 
with  studies  of  the  movement  of  water  under 
the  stress  of  such  a  sudden  cataclysm.  The 
canals  and  irrigating  works  already  existing 
in  Lombardy  were  enormously  improved  by 
his  hydraulic  knowledge,  and  his  contrivances 
were  still  employed  by  the  Milanese  at  the 
end  of  the  seventeenth  century.  He  ex- 
perimented on  the  lines  which  subsequently 
produced  the  "  camera  obseura,"  and 
initiated  the  theory  of  complementary 
colours  which  was  carried  on  by  Chevreuil. 

Of  his  numberless  mechanical  inventions, 
it  will  be  sufficient  to  say  that  he  designed  a 
breech-loading  cannon  which  propelled  its  ball 
by  steam,  that  he  invented  paddle-wheels  for 
boats,  and  that  he  suggested  the  use  of 
parachutes  and  of  screws  turning  on  a  vertical 
axis  as  a  means  of  aerial  locomotion.  Other 
details  will  appear  in  their  right  place,  when  I 
come  to  point  out  more  emphatically  those 
investigations  into  spiral  forms  in  Leonardo's 
manuscripts  which  are  especially  appropriate 
to  the  subject  of  this  book.     But  I  have  said 


i.]  STUDIES  IN  NATURE  25 

enough  already  to  remove  any  improbability 
from  the  suggestion  that  as  an  architect 
Leonardo  would  be  likely  to  show  traces  of 
his  studies  in  other  directions,  and  I  can  now 
pass  on  to  consider  more  closely  the  form 
and  meaning  of  various  kinds  of  spirals. 

Besides  collecting  and  examining  some 
spiral  formations  in  Nature,  with  the  object 
of  discovering,  if  possible,  any  principles 
that  may  underlie  their  existence  and  con- 
struction, I  shall  call  attention  to  those 
formations  in  Art  which  may  appear  to  be 
more  particularly  connected  with  this 
subject;  and  it  will  thus  be  possible  to 
realise  a  little  better  the  full  value  and 
meaning  of  the  architectural  example  with 
which  this  book  concludes.  The  attribution 
of  a  certain  staircase  to  a  certain  master  may 
not  interest  many  beyond  a  restricted  class 
of  readers ;  but  the  steps  by  which  that 
attribution  is  arrived  at,  and  the  artistic 
principles  of  which  that  staircase  is  a  type, 
are  matters  that  should  appeal  to  the  far 
larger  audience  to  whom  questions  of  taste 
and  of  abstract  beauty  are  not  limited  by  the 
requirements  of  a  single  profession  or  a  single 
branch  of  knowledge. 


CHAPTER  II 


OF    SPIRALS 


what 


"Search  where, thou  wilt  and  let  thy  Reason  go 
To  ransome  Truth  even  to  th'  Abyss  below  ; 
Rally  the  scattered  Causes,  and  that  line 

Which  Nature  twists,  be  able  to  untwine." 


T3EFORE  me  as  I  write  is  a  plain 
.  cylinder  of  wood,  nine  inches  high, 
with  a  diameter  of  just  over  one 
inch  (fig.  3).  I  have  taken  a  piece 
of  string  eighteen  inches  long  and 
nailed  it  to  the  bottom  edge,  in 
order  to  wind  it  round  the  cylinder 
to  the  top  edge.  In  doing  this,  I 
find  it  easier  and  more  natural  to 
make  the  first  turn  of  the  string 
towards  the  right,  with  the  result 
that  the  three  visible  lines  of  the 
string  made  by  its  ascent  upon  the 
cylinder  are  all  curves  which  move 
upwards  towards  the  right,  and 
these  curves  are  in  the  form  of 
is  called  a  spiral,  and  sometimes  a  helix. 


chap.il]    RIGHT-HANDED   FENCING  27 

When  I  rotate  the  cylinder  on  its  axis  they 
remain  the  same.  In  this  instance  I  have 
formed  a  right-handed  (or  dextral)  cylindrical 
spiral  (see  fig.  27).  When  a  watch-spring  lies 
flat  upon  the  table  it  forms  a  plain  spiral  (see 
figs.  34,  85).  If  you  fix  its  largest  circle  to 
the  table,  and  raise  up  its  innermost  point, 
you  find  that  a  conical  spiral  has  been  formed  ; 
and  a  good  natural  example  of  this  is  shown 
in  Mitra  papalis  (fig.  26).         • 

At  the  same  point  on  the  bottom  edge  of 
the  cylinder  where  I  had  fixed  my  string, 
I  now  fix  a  piece  of  flat  narrow  tape  of 
precisely  the  same  length,  so  that  I  can 
wind  it  round  the  cylinder  to  the  same  point 
on  the  top  edge  reached  by  the  string.  I 
had  naturally  wound  to  the  right  before, 
because  my  right  hand  (being  that  of  a  right- 
handed  man)  always  finds  it  easier  to  make 
a  circle  towards  the  right  than  towards  the 
left,  just  as  every  right-handed  fencer  knows 
that  the  contre-sixte  is  an  easier  parry  than  the 
contre-quarte,  because  the  circular  movement 
of  the   hand   is   towards  the  right,  whereas1 

1  In  driving,  the  instinctive  movement  of  the  hand 
would  turn  a  horse  to  the  right  when  passing  an  obstacle 
in  its  way,  and  most  nations  are  content  that  this  should 
be  so,  although  the  coachman's  seat  is  placed  over  the 
right  wheel.  The  English,  however,  have  logically  over- 
come their  instincts  and  drive  to  the  left ;  they  prefer  to 
see  where  their  right  wheel  is  going. 


28  OF   SPIRALS  [chap. 

Kirchhoffer,  a  left-handed  man,  is  celebrated 
for  his  contre-quarte. 

I  now  begin  by  turning  my  tape  to  the 
left,  and  when  it  is  fixed  at  the  top,  I 
find  its  three  ascending  curves  go  up  by  a 
different  and  symmetrically  opposite  path  to 
that  taken  by  the  string;  I  have  made,  in 
fact,  a  cylindrical  spiral,  which  is  not  of  the 
usual  dextral  or  right-handed  form,  but 
sinistral  or  left-handed.  The  difference  seems 
very  simple  when  it  is  expressed  in  simple 
language,  but  it  will  have  to  be  kept  very 
carefully  in  mind  in  the  course  of  these  pages, 
for  a  good  deal  will  be  found  to  depend 
upon  it.  So  much,  indeed,  is  this  the  case, 
that  I  find  it  impossible  to  proceed  without 
placing  my  cylinder  upright  on  the  table 
before  me,  with  the  two  different  threads  of 
string  and  tape  clearly  showing  the  difference 
between  the  two  forms  of  spiral ;  and  I  notice 
it  does  not  matter  which  end  of  the  cylinder  is 
at  the  top,  for  the  spirals  remain  the  same  if 
I  stand  it  upside  down ;  and  this  may  also  be 
prettily  demonstrated  by  reversing  this  book 
and  looking  at  the  staircases  shown  in  figs. 
28,  55  and  59,  from  the  top  instead  of  from 
the  bottom,  a  point  of  view  which  will  indeed 
only  emphasise  the  complicated  beauty  of 
their  construction. 

The   beautiful   effect    obtained   in   wrhat   is 


II.] 


NATURAL  BUILDING 


29 


known  as  the  "  Prentice's  Pillar,"  in  Rosslyn 
Chapel  (fig.  4)  is  due 
to  the  fact  that  its 
separate  right  -  handed 
spirals  (proceeding  from 
their  separate  points) 
envelop  in  their  long 
and  slender  ascending 
curves  a  pillar  which 
is  artfully  grooved  in 
perpendicular  lines,  so 
that  full  value  may  be 
given  to  the  encircling 
decoration.  In  Nature 
the  ascending  curves  of 
spiral  growth  are  nearly 
always,  like  these,  to- 
wards the  right,  as 
shown  by  the  Pillar 
and  by  the  string  upon 
my  cylinder,  when  ob- 
served at  right  angles 
to  its  elevation.  Either 
very  rarely  in  a  "  sport," 
or  with  some  definite 
reason  in  artificial  ex- 
amples, the  ascending 
curves  are  those  towards  F,G'  4' 

the     left,    as     Shown     by  ^  Up-ntice'sPillar"atEosslya. 

the  tape  when  its  course  is  followed  from  the 


SO  OF  SPIRALS  [chap. 

bottom  ot  the  cylinder  upwards.  Such 
reverse  curves  a  right-handed  man  makes 
with  conscious  effort  either  with  his  right 
hand  or  right  foot ;  they  seem  in  fact  to 
be  chiefly  connected  with  descent,  and  may 
be  observed,  under  certain  circumstances,  in 
the  fall  of  a  strong  stream  of  water  from  a 
height.  We  should  not  expect  them,  there- 
fore, to  occur  in  architecture,  because  man 
builds  upwards,  and  his  upward  spiral 
movement  would  be  instinctively  to  the  right 
as  it  is  in  the  "  Prentice's  Pillar." 

In  the  Chapel  of  the  Holy  Innocents  in  the 
Crypt  of  Canterbury   Cathedral   (beneath    St 
Andrew's  Chapel)  there  is  a  short  column,  with 
a  shaft  four  feet  in  height,  showing  spiral  bands 
running  upwards  to  the  right  with  very  fine 
effect ;  and  it  is  curious  that  the  same  crypt 
provides  an  interesting  example  (in  St  Gabriels 
Chapel,   beneath    St   Anselm's   Tower)    of    a 
column  with  a  shaft  five  feet  in  height,  which 
begins  with  a  left-handed  spiral  in  its  grooved 
decorations,  but,  half  way  up,  these  grooves  are 
changed  to  a  right-handed  spiral,  with  a  band 
of   irregular    incised   diamonds   to   mark  the 
transition,  as  if  the  workman  had  felt  that  the 
design  had  been  begun  wrongly,  and  had  there- 
fore corrected  its  direction.     This  was  built  in 
1103,  and  in  1121  a  further  development   in 
spiral   decoration   is   observable   in  the   same 


il]  CANTERBURY  CRYPT  31 

building.  If  you  stand  in  front  of  the  Lady 
Chapel  in  St  Ernulf 's  Crypt,  and  look  west- 
wards down  the  central  alley,  you  will  see  eight 
pairs  of  columns,  of  which  the  second,  fourth, 
sixth,  and  last  exhibit  a  spiral  arrangement  of 
grooves.  In  the  first  two  a  right-handed  spiral 
is  elaborately  decorated  throughout.  In  the 
next  pair,  the  bands  of  decorations  are  cut 
alternately  in  right-handed  and  left-handed 
spirals,  and  end  in  straight  fluted  grooves. 
The  left-handed  arrangement  is  never  per- 
mitted to  stand  alone  ;  from  which  we  may 
perhaps  infer,  that  if  there  was  one  left-handed 
man  among  the  masons,  his  right-handed 
comrades  took  care  that  he  should  never  com- 
plete a  design  which  did  not  fall  in  with  their 
idea  of  what  was  appropriate  to  the  principles 
of  growth,  support,  or  strength,  typified  by  a 
column  (see  p.  96). 

The  commonest  instance  of  a  cylindrical 
spiral  is  the  homely  corkscrew,  which  may 
be  placed  for  comparison  beside  our  cylinder 
of  tape  and  string,  and  it  will  be  seen  that 
its  masculine  strength  of  penetration  is  ex- 
pressed by  the  same  right-handed  curves  as 
those  of  the  string.1     If  you  place  it  upright 

1  I  need  hardly  perhaps  remind  the  traveller  that  he 
would  never  have  got  across  the  Rocky  Mountains  in  a 
railway  train  if  the  track  had  not  been  planned  on  a 
feasible  gradient  by  the  scheme  of  spiral  tunnels  gradually 
ascending  like  a  corkscrew. 


32  OF  SPIRALS  [chap. 

upon  its  point,  you  will  observe  that  an  insect 
ascending  to  the  handle  would  be  perpetually 
turning  to  the  left,  so  conchologists  call  this 
spiral  "  leiotropic,"  for  they  seem  to  have 
connected  shells  and  staircases  together  as 
soon  as  scientific  terminology  became  common. 

If  you  imagine  that  the  string  surrounding 
our  cylinder  is  made  of  the  same  substance 
as  the  cylinder,  and  projects  a  little  further 
from  the  surface,  you  will  have  an  example 
of  the  ordinary  screw.  The  coffin-screw,  on 
the  other  hand,  is  that  fortunately  rarer 
variety  which  only  penetrates  when  it  is 
turned  in  the  unusual  direction,  to  the  left. 
In  these  military  days  it  is  also  possible  to 
point  to  a  sinistral  spiral  which  has  become 
a  common  object  of  admiration,  and  that  is 
the  rifling  in  a  Lee-Metford,  which  is  made 
to  turn  to  the  left  in  order  to  counteract 
the  pull  of  the  average  right-handed  soldier. 
It  is  curious  that  all  left-handed  spirals  look 
as  if  they  were  at  almost  double  the  pitch 
of  the  corresponding  right-handed  spirals ; 
perhaps  because  they  are  less  familiar  to  the 
eye. 

A  screw  may  be  defined  as  a  cylinder  of 
wood  or  metal  having  a  spiral  ridge  ( "  the 
thread " )  winding  round  it,  usually  turning 
in  a  hollow  cylinder,  in  which  a  spiral  channel 
is     cut    corresponding    to    the    ridge.      The 


ii.]  SHAVINGS  S3 

distance  between  the  medial  lines  of  any  two 
successive  threads  of  a  screw,  measured  in  a 
direction  parallel  to  the  axis,  is  called  "the 
pitch  "  of  the  screw.  A  "  screwstone  "  is  the 
name  sometimes  given  to  one  of  the  joints 
of  the  stem  of  an  encrinite,  or  "  stone-lily," 
a  Palaeozoic  crinoid  plentifully  found  in 
marble,  and  belonging  to  a  class  of  animals 
(echinodermata)  which  are  stalked,  or  fixed 
like  a  plant  for  some  or  all  of  their  lives.  A 
"  Portland  screw  "  is  a  similar  name  bestowed 
on  the  fossil  cast  of  the  interior  of  Cerithium 
Portlandicum.  The  name  of  "Augur-shell" 
has  for  the  same  reason  been  given  to  a 
toxoglossate  gastropod  called  Terebra  (Bullia) 
semiplicata,  and  more  especially  to  T. 
maculata. 

As  we  shall  see  when  we  come  to  consider 
the  origin  of  spiral  shells,  the  force  which 
determines  the  original  direction  may  be  very 
slight  and  subtle,  yet  is  invariably  "good 
evidence."  The  shape  of  the  shavings  at  a 
carpenter's  bench,  for  instance,  might  furnish 
another  Sherlock  Holmes  with  the  proof  he 
required  that  his  murderous  mechanic  was 
either  left-handed  or  a  Japanese ;  for  one  of 
these  two  he  must  have  been  if  the  shavings 
exhibit  a  sinistral  spiral.  The  right-handed 
screw  which  is  usual  in  the  innocent  shaving 
is  produced  because  the  right-handed  carpenter 


34  OF  SPIRALS  [chap. 

invariably  drives  his  plane  a  little  to  the  left. 
Orientals  seem  always  to  prefer  a  left-handed 
spiral,  just  as  they  write  from  right  to  left, 
and  a  common  example  may  be  found  in  those 
silver-headed  walking-sticks  of  blackwood 
which,  in  all  instances  I  know,  are  carved  in 
left-handed  spirals,  where  a  Western  workman 
would  naturally  have  turned  them  to  the 
right.1 

Many  of  the  walking-sticks  sold  to  our 
officers  in  South  Africa,  and  made  by  Zulus, 
are  carved  into  a  sinistral  spiral,  but  it  is 
impossible  for  me  to  say  whether  this  is  owing 
to  left-handed  workmanship,  or  to  imitation 
of  a  climbing  plant  which  coils  (like  our  own 
hop)  in  a  left-handed  spiral.  I  was  at  first 
inclined  to  think  that  the  persistence  of  the  left- 
handed  twist  in  prehistoric  Irish  torques,  as 
may  be  seen  from  examples  from  Dublin,  and 
in  the  British  Museum,  was  due  either  to  the 
predominance  of  left-handedness  in  Ireland, 
which  is  shown  by  the  use  of  the  light  left- 
hand  axe  mentioned  by  Giraldus  Cambrensis, 
or  to  the  fact  that  the  most  skilful  artificers 
were  developed  from  left-handed  men.  But 
nothing  is  so  strange  about  spiral  formations 
as  the  results  of  practical  experience,  and    I 

1  An  interesting  comparison  may  be  found  in  the  spiral 
twist  which  forms  so  common  an  ornament  in  Swedish 
silver  spoons. 


il]  TORQUES  35 

soon  found  that  the  flat  ribbon  of  soft  gold 
from  which  the  earliest  torques  are  made, 
would  naturally  become  a  left-handed  spiral  if 
twisted  by  a  right-handed  man,  for  he  would 
hold  down  one  end  with  his  left  hand,  and 
would  twist  the  other  end  outwards  with  his 
right  hand,  with  the  result  that  the  spiral  of 
the  twisted  gold  would  be  left-handed,  as  may 
be  proved  by  any  one  with  a  long  piece  of 
narrow  paper.  This  may  account  for  the  fact, 
that  from  the  many  torques  I  have  examined, 
all  the  gold  examples  were  left-handed,  the 
only  right-handed  spiral  shown  being  a  silver 
specimen  in  the  Germania  Museum  at  Nurem- 
berg, and  another  silver  specimen  now  in  the 
Society  of  Antiquaries.  The  five-coiled  arm- 
let in  the  British  Museum,  exhibits  the  usual 
left-handed  twist,  but  has  the  additional  charm 
of  showing  four  distinct  spirals,  which  has 
resulted  from  the  use  of  four  flat  ribbons 
of  gold  united,  the  combined  section  being 
cruciform  before  the  process  of  twisting  had 
begun. 

The  use  of  this  spiral  formation  as  an 
honourable  ornament  is  certainly  as  old  as  the 
golden  collar  promised  by  Belshazzar  as  a 
reward,  the  Chaldee  name  for  which  was 
Meneka,  transliterated  in  the  Septuagint  (Dan. 
v.  7),  as  Maytag.  From  the  Chaldseans  this 
form  passed  to  the  Persians,  and  the  mosaic 


36  OF   SPIRALS  [chap 

pavement  from  Pompeii,  now  in  the  Naples 
Museum,  represents  Darius  and  his  officers  at 
the  battle  of  Arbela,  wearing  torques  which 
end  not  in  the  usual  cones,  but  in  snakes' 
heads.  The  crest  of  the  Manlius  family  in 
Rome  had  its  origin  in  the  prowess  of  T. 
Manlius  Torquatus,  who  beat  a  Gaul  in  single 
combat,  and  took  from  him  the  torque  which 
had  descended  to  his  nation  as  an  honourable 
symbol  from  Chaldsean  sources,  and  which 
passed  on  to  Druids  and  Celts  in  the  British 
Islands  in  the  various  forms  that  are  now 
discovered  in  their  tombs.  The  collar  itself 
(though  not  its  spiral  form)  continues  to  be  a 
mark  of  honour  to  the  present  time,  among 
Knights  of  the  Garter,  or  the  Golden  Fleece, 
and  even  among  provincial  Mayors.  Indeed, 
the  phrase  "  Collar-day,"  as  an  ordinary  con- 
comitant of  courtly  ceremonial,  is  to  be 
found  in  almost  any  issue  of  the  Lord 
Chamberlain's  instructions  for  "  red-letter " 
days,  when  there  are  special  Collects,  Epistles, 
and  Gospels  said  in  Church,  and  when  the 
judges  wear  red  in  the  Courts.  The  only 
difference  between  the  modern  insignia  of  rank 
and  the  Celtic  torque,  is  the  loss  of  the  signi- 
ficance involved  in  the  spiral  form  of  the 
primitive  decoration. 

The   Investigations  of  the  Anthropological 
Society   of  Washington    (May    1879)    go    to 


il]  LEFT-HANDED   MEN  37 

show  that  though  left-handed  workmen 
existed  in  the  Palaeolithic  Age,  prehistoric  man 
was  as  a  rule  right-handed.  The  buttons  of 
our  own  dress,  like  the  hooks  and  eyes  of  our 
ladies'  attire,  are  now  expressly  adapted  to  the 
right  hand.  So  are  the  adze,  the  plane,  the 
gimlet,  the  cutting  end  of  the  augur,  the 
scythe,  the  fittings  of  a  rifle,  scissors,  snuffers, 
shears,  and  other  mechanical  tools  which  must 
be  used  by  one  hand  or  the  other ;  or,  when 
used  by  several  men  at  once,  must  be  used  by 
the  same  hand  in  each  man.  All  this,  how- 
ever, will  not  prevent  one  who  is  naturally  left- 
handed  from  continuing  his  natural  practice, 
though  it  is  attended  by  great  mechanical 
inconvenience  in  all  the  instances  mentioned. 

A  man  with  only  a  slight  bias  towards  his 
left  hand  will  readily  become  ambidextrous 
owing  to  the  many  right-handed  conventions 
and  appliances  which  occur  in  everyday  life. 
But  the  instinctively  and  strongly  left-handed 
will  never  change,  and  is  usually  distinguished 
for  his  skill,  as  Sir  Daniel  Wilson  has  pointed 
out  in  his  interesting  monograph  on  the 
subject.  When  Gideon  discomfited  the  hosts 
of  the  Amalekites,  the  seven  hundred  Ben- 
jamites  he  selected  for  their  superior  skill 
in  slinging   were   all   left-handed.1     Only  the 

1  Compare  the  chapter  on  "  The  Right  and  Left  Hand/' 
in  Sir  Thomas  Browne's  "Vulgar  Errors/'  IV.  v. 


38  OF   SPIRALS  [chap. 

best,  in  fact,  of  the  left-handed  men  can 
survive  in  the  struggle  against  the  vast 
majority  of  right-handed  influences  around 
them,  and  their  skill  will  go  on  increasing,  as 
may  be  seen  in  the  case  of  left-handed  fencers 
who  have  far  more  opportunity  of  practising 
against  right-handed  men  than  we  have  of 
getting  used  to  them. 

It  is  worth  noticing  in  this  connection  that 
when  Londoners  had  an  opportunity,  in 
March  1902,  of  seeing  eight  of  the  best  fencers 
in  the  world,  of  whom  four  Italians  were  pitted 
against  four  Frenchmen,  the  pair  who  did 
best  of  all  were  the  two  famous  French  left- 
handers, Louis  Merignac  and  Kirchhoffer. 
Indeed,  instead  of  starting  at  a  disadvantage, 
as  is  too  often  assumed,  a  left-handed  artist 
has  generally  the  advantage  of  his  right- 
handed  rivals,  for  he  is  usually  ambidextrous 
by  education,  besides  being  possessed  of 
a  high  degree  of  congenital  skill  in  the 
hand  he  prefers,  as  may  be  seen  in  the 
instance  of  Leonardo  da  Vinci  or  of  Hans 
Holbein. 

It  is  probable  that  when  it  was  not  a  matter 
of  importance  for  a  helix  to  be  either  dextral 
or  sinistral,  the  first  sketch  for  such  a  helix 
made  by  a  left-handed  man  would  more  often 
exhibit  a  sinistral  than  a  dextral  spiral ;  but 
when  we  come  to  an  example  of  a  sinistral 


ii.]  NARWHALS  39 

helix  which  may  have  been  designed  by 
Leonardo  da  Vinci,  I  do  not,  therefore,  wish 
to  argue  that  his  skill  in  drawing  with  his  left 
hand  was  alone  responsible  for  the  rarer 
formation.  The  fact  that  he  was  left-handed 
may  certainly  have  suggested  the  original 
form  of  the  left-handed  helix  which  he  eventu- 
ally elaborated  for  other — and  more  potent — 
reasons. 

Dr  Wherry  has  pointed  out  that  right- 
handedness  or  left  -  handedness  sometimes 
leave  definitely  traceable  effects  in  the  works 
of  early  or  unskilled  artists.  In  the  archaic 
bust  of  an  Apollo  forty-seven  curls  out  of 
sixty-one  turned  the  way  of  the  clock-hands. 
In  another  statue,  dating  before  the  Persian 
war,  the  curls  are  arranged  in  right-  or  left- 
handed  spirals,  according  to  the  side  of  the 
head  on  which  they  grow,  not  as  in  Nature. 

I  have  mentioned  the  slight  causes  which 
may  give  an  apparently  accidental  origin  to  a 
spiral.  The  follicle  of  hair  is  a  good  example 
of  this.  In  Western  peoples  it  is  generally 
straight,  but  in  the  negroid  races  the  follicle 
is  bent,  and  the  result  is  the  spiral  shown  in 
curly  hair.  The  socket  of  a  tusk  or  the  base  of 
a  horn  has  much  the  same  effect  on  growth. 
The  two  examples  of  narwhal's  tusk  (really  his 
front  tooth),  which  I  have  chosen  from  the 
Museum   of  the  Royal    College  of  Surgeons 


40  OF   SPIRALS  [chap. 

(fig.  5),  show  excellently  the  rare  sinistral 
spiral,  and  the  variation  shown  by  the 
additional  curves  in  one  of  them  is  no  doubt 
due  to  a  slight  variation  in  the  socket. 
Every  narwhal  tusk  I  have  ever  seen  (and 
there  are  six  now  in  one  naturalist's  shop  in 
Oxford  Street)  has  a  left-handed  spiral,  in- 
cluding a  sixteenth  century  carved  specimen, 
now  in  the  Sala  dei  Stucchi  of  the  Doges' 
Palace,  and  another  still  older  tusk,  preserved 
in  St  Mark's  Treasure,  in  Venice.  But  they 
exhibit  an  even  more  extraordinary  partiality 
to  this  formation.  There  are  seven  examples 
known  of  narwhals  with  a  double  tusk. 
One  of  these  is  in  the  British  Museum 
of  Natural  History  at  South  Kensington. 
Instead  of  following  the  examples  of  the  horns 
I  mention  later  (p.  80),  and  showing  differ- 
ent spirals,  this  pair  of  tusks  exhibits  two 
spirals  of  the  same  kind,  and  each  of  them 
is  sinistral ;  and  though  I  only  speak  of  what 
I  have  myself  examined,  the  statement  has 
been  made  that  whenever  a  narwhal  has  two 
teeth  their  spirals  are  identical,  instead  of 
exhibiting  symmetrically  different  spirals 
about  the  middle  plane  of  the  body,  as  might 
have  been  expected.  Dr  Wherry  thinks  that 
as  an  unerupted  tusk  exhibits  a  perfectly 
straight  fibre,  the  direction  of  the  spiral 
is    formed    after    it    leaves     the     bone    and 


-'  - 


Fig.  5. 

Narwhal's  tusks. 


Fig.  6. 

Elephant's  distorted  Tusk. 
[To  face  page  41. 


ii]  PHARAOHS   SERPENTS  41 

becomes  opposed  to  the  waves  during  growth, 
owing  to  the  fact  that  the  creature  "plays" 
to  one  side  as  it  ploughs  through  the  water ; 
and  when  by  a  rare  chance  two  tusks  are 
developed,  the  creature  preserves  the  habit 
of  carrying  its  head  on  one  side  and  so 
gives  both  tusks  the  sinistral  twist  it  gives  to 
one.  In  the  Museum  of  the  Royal  College  of 
Surgeons  I  found  an  elephant's  tusk  (fig.  6) 
which  exhibits  a  very  abnormal  form  indeed, 
for,  instead  of  being  the  usual  segment  of  a 
circle,  the  tusk  has  grown  into  a  sinistral 
spiral,  so  much  accentuated  by  causes  latent 
in  the  socket  that  the  whole  thing  has  taken 
a  complete  corkscrew  formation.1  That  an 
alteration  in  the  socket  is  quite  sufficient  to 
control  the  formation  of  a  growing  spiral  may 
be  proved  by  placing  one  of  the  eggs  called 
"  Pharaoh's  serpents "  in  a  small  tube.  As 
soon  as  the  spiral  begins  to  come  out  of  the 
egg  it  will  exhibit  a  dextral  helix  if  the  tube 
is  dented  slightly  on  the  left,  and  a  sinistral 
helix  when  the  orifice  of  the  tube  has  a  dent 
upon  the  right. 

Another  example  of  the  spiral  arrangement 
in  teeth  is  so  curious  that  it  must  be  inserted 

1  Frank  Buckland  had  certain  rabbits'  teeth  in  his 
collection  which  had  grown  into  a  spiral  form  owing  to  an 
injury  at  their  base  from  a  stray  shot  or  some  other 
accident. 


42  OF   SPIRALS  [chap. 

here.  In  the  Imperial  School  of  Mines  at 
St  Petersburg  is  a  fossil  which  has  been  given 
the  misleading  name  of  Helicoprion.  A  cast 
of  it  is  placed  among  the  fossils  at  the  British 
Museum  in  South  Kensington.  In  general 
shape  it  very  much  recalls  the  form  of  the 
section  of  the  Ammonite  shown  in  fig.  366, 
but  a  closer  examination  shows  that  it  is  really 
a  row  of  sharp  teeth  set  upon  a  ribbon  which 
is  spirally  constricted  into  that  form.  On  the 
drawing  of  the  logarithmic  spiral  in  fig.  35, 
1  have  placed  letters  that  will  explain  the 
growth  of  this  queer  fossil,  which  has  now 
been  proved  to  be  a  single  transverse  row  of 
teeth  from  the  jaw  of  an  Elasmobranch  fish. 
The  new  growth  comes  from  the  point  A  ; 
the  teeth  are  used  for  biting  at  the  point  B ; 
and  as  they  become  worn  out  they  move  back 
in  a  spiral  direction,  the  small  teeth  of  the 
young  fish  being  naturally  in  the  centre  of 
that  spiral  at  C,  and  the  larger  teeth  of  the 
growing  fish  being  at  A. 

An  analogous  case  of  this  strange  folding-up 
of  disused  teeth  is  to  be  found  in  Cochliodus 
contortus,  a  shark-like  fish  from  the  carboni- 
ferous limestone,  with  crushing  teeth  instead 
of  the  pointed  teeth  of  Helicoprion;  and  a 
very  similar  arrangement  of  growTth  may  be 
observed  in  the  teeth  of  the  Skate,  which  grow 
at  A,  are  used  at  B,  and,  after  beginning  a 


ii.]  RARE   FORMS  43 

spiral  curve,  fall  away  before  reaching  any- 
where near  the  point  C — a  much  more  con- 
venient arrangement,  it  would  seem,  than 
that  of  carrying  disused  teeth  coiled  up  some- 
where in  the  head,  as  must  have  been  the  case 
with  Helicoprion. 

The  difference  between  such  dextral  and 
sinistral  spirals  as  we  have  now  seen  artificially 
constructed,  "from  the  outside,"  will  become 
more  and  more  suggestive  when  we  investigate 
a  few  examples  of  spiral  growth  "  from  with- 
in "  in  plants  and  other  natural  objects ;  and 
we  shall  find  that  when  objects  which  usually 
display  a  dextral  helix  are  found  to  show  a 
sinistral  helix,  some  peculiar  value  and  often 
some  supernatural  signification  is  attached  to 
them  by  the  primitive  races  who  make  the 
first  discovery.  The  delight  in  such  rarities 
of  Nature,  and  the  instinctive  use  of  them  as 
ornament,  was  shown  by  Schliemann  to  be  at 
least  as  old  as  ancient  Troy ;  for  he  found  that 
an  inland  people  had  used  the  echinus  or  sea- 
urchin  as  a  model  for  the  bosses  which  they 
set  round  the  circle  of  their  shields. 

A  still  more  interesting  example,  which 
has  left  easily  verifiable  traces  at  the  present 
time,  is  the  belief  of  the  inhabitants  of 
Travancore  that  the  sacred  shell  called 
"  Sankho  "  is  a  manifestation  of  the  god  Vishnu, 
because  its  internal  spiral  does  not  turn  to  the 


44 


OF   SPIRALS 


[chap. 


right  (with  its  "  entrance  "  therefore  also  to  the 
right),  as  in  the  case  of  the 
shell  Turbinella  pirum  (fig. 
7),  and  in  a  million  other 
examples,  but  turns  to  the 
left  (with  its  "entrance" 
also  to  the  left)  as  in  Tur- 
binella rapa  (see  fig.  8)  with 
the  rare  sinistral  helix  ;  and 
this  belief  survives  in  the 
drawing,  conventionalised 
though  it  be,  of  this  sacred 
fig.  7.  shell   (with   its   opening  to 

TurUneiia  pirum.       the  left)  which  is  to  be  seen 

upon    the    postage    stamps 

now    used    in     Travancore 

(see  fig.  9).    This  Turbinella 

rapa,    called    the    "  chank 

shell/'     is     represented     in 

Hindoo  religious  art  as  held 

in  the  hand  of  Vishnu.     It 

is  fished  for  at  Tuticorin  on 

the  Gulf  of   Manaar   from 

October    to    May,    and    in 

1887  a  good  sinistral  speci- 
men  found   at    Jaffna   was 

sold  for  Rs.700.     Nearly  all 

the   shells   brought   up   are 

sent  to  Dacca  to  be  sliced  into  bangles  and 

anklets  for  Hindoo  women ;  and  this  use  of 


Fig.    8. 

Turbinella  rapa. 


II.] 


USEFUL   SHELLS 


45 


shells  as  ornaments  among  savage  inland 
races,  and  more  civilised  dwellers  by  the  sea, 
may  be  paralleled  in  every  quarter  of  the 
globe  in  the  earliest  periods  of  time.  In  the 
Indian  Ocean  Cypraea  moneta  (the  "  money- 
cowry")  has  for  ages  been  employed  as  a 
medium  of  exchange,  as  is  Cypraea  annulus 
in  the  Pacific.  In  Bengal  in  1854,  the  value 
of  5,120  cowries  came  to  one  rupee.  In 
Egypt  the  same  shell  is  still 
considered  to  be  a  preservative 
against  the  "evil  eye." 

The  use  of  the  spiral  in 
ornament  goes  back  to  pre- 
historic times  in  other  in- 
stances. In  the  work  of  the 
Bronze  Age  flat  spirals  are 
found  hanging  to  the  side  of 
a  shield  as  decorations,  just 
as  on  an  ancient  Pile- Hut- Urn  (which  is 
mentioned  in  Sir  John  Lubbock's  "Pre- 
historic Times,"  and  is  thought  to  come 
from  Melos)  the  walls  of  the  house  are 
represented  as  being  decorated  with  large 
spirals ;  and  Mr  Arthur  Evans  found  a  frieze 
of  spirals  and  rosettes  painted  on  the  walls 
of  the  Palace  of  Minos  at  Knossos  in 
Crete.  From  the  well-known  fact  that  the 
mediaeval  monks  used  to  say  their  prayers 
within  a  maze,  to  escape  the  pursuit  of  the 


Fig.  9. 


Postage  Stamp  now  used 
at  Travancore. 


46  OF   SPIRALS  [chap. 

Devil,  the  spirals  tattooed  upon  a  Maori's 
face  may  have  the  same  object  of  confusing 
the  Evil  One,  though  it  may  quite  as  possibly 
be  a  result  of  his  inborn  sense  of  the  adapta- 
tion of  ornament  to  form ;  for  his  spirals 
admirably  express  the  feature  decorated,  and 
seem  to  do  so  in  a  way  which  concentric 
circles  never  can.  Spirals  are  found  in  the 
decorative  art  of  such  different  peoples  as  the 
natives  of  New  Guinea  (especially  where 
Melanesian  influence  occurs),  of  Borneo,  of 
ancient  Peru,  of  Central  Africa.  Sometimes 
the  form  is  connected  with  the  manufacture  of 
pottery  or  basketwork,  and  it  is  then  definitely 
suggested  by  the  structural  lines  of  the  object. 
Often  the  spiral  seems  the  genuine  expression 
of  artistic  feeling  or  fanciful  imagination.  But 
in  no  case  do  we  find  a  savage  making  an 
abstract  pattern  that  does  not  go  back  to 
Nature  by  a  series  of  conventional  variations. 
All  forms  of  the  spiral  in  Polynesia,  for 
instance,  can  be  traced  to  a  Malay  centre,  and 
that  centre  took  its  ornaments  from  Hindoo 
or  Phoenician  sources. 

No  doubt  the  discovery  of  bronze  was  a 
most  substantial  step  in  the  progress  of 
civilization,  inasmuch  as  this  discovery  en- 
abled the  men  of  the  Stone  Age  in  Northern 
Europe  to  learn  such  patterns  as  the  chevron, 
the  meander,  and  the  spiral  scroll,  at  the  same 


ii]  THE   LOTUS  47 

time  as  they  learnt  the  arts  of  metal-working. 
Patterns  grow :  they  are  not  made.  They 
are  evolved  from  pictures,  and  from  those 
pictures  which  most  often  occur,  and  are  most 
easily  repeated.  Among  such  pictures,  those 
which  represented  the  lotus  would  be  as 
significant  and  as  sacred  as  any  known  to  the 
earliest  periods  of  Egyptian  art.  The  earliest 
pictures  were  not  done  for  their  own  sake,  as 
"  works  of  art."  They  were  meant  to  convey 
an  idea;  they  were  even  supposed  to  retain 
some  of  the  powers  and  qualities  of  the 
original.  So  the  lotus,  as  the  emblem  not 
of  one  god  but  of  all,  not  of  one  sacred 
animal  but  of  all,  embodied  an  enormous 
amount  of  ancient  and  popular  symbolism, 
and  supplied  patterns  to  paleolithic  peoples, 
whose  pictures  we  know  to  have  been  life-like 
representations  of  the  incidents  of  the  chase. 

Spiral  scrolls  have  been  found  on  pottery  in 
Schliemann's  "  First  Tomb  "  at  Mycenae  ;  on 
scarabs  of  an  Egyptian  dynasty  which  existed 
three  thousand  nine  hundred  years  before 
Christ ;  on  bronze  axe-heads  from  pre-historic 
Sweden.  Mr  Henry  Balfour  possesses  many 
examples  in  the  Pitt  Rivers  Museum  at 
Oxford.  At  Leyden  the  representative  ex- 
hibit for  the  Malay  Archipelago  is  unique.  The 
ethnographic  collections  in  Washington,  in 
Rome,  and  Amsterdam,  are  also  full  of  similar 


48  OF   SPIRALS  [chap. 

specimens.  Throughout,  the  theory  of 
spontaneous  generation  falls  to  the  ground. 
The  rule  of  historic  development  and  tradition 
shows  no  exception ;  and  Professor  W.  H. 
Goodyear  has  very  carefully  investigated  the 
whole  subject  as  suggested  to  him  first  by 
the  geometric  lotuses  upon  the  Cypriot  vases. 
He  showed  that  all  the  Arab  and 
Mohammedan  spirals  came  from  the 
Byzantine  Greeks ;  that  they  are  not  found 
at  all  in  barbaric  Africa,  and  that,  on  the 
other  hand,  they  are  the  foundation  of  Malay 
ornament ;  they  reached  Alaska,  however, 
by  means  of  Buddhist  influence,  along  the 
Amory  valley,  through  the  Yakoots  to  the 
Aleutian  islands.  When  it  is  realised  that  five- 
sixths  of  the  ornamental  patterns  of  ancient 
Egyptian  art  were  based  upon  the  lotus  and 
its  spiral  derivatives,  the  number  of  spiral 
traditions  which  spread  from  the  Nile  valley 
all  over  the  world  will  be  better  understood. 
The  oldest  forms  of  the  spiral  associated  with 
the  lotus  are  found  in  Egyptian  tomb-ceilings. 
The  Greeks  and  Assyrians,  who  found  the 
flower  already  conventionalised  almost  out  of 
knowledge,  took  the  spiral  accompaniments 
and  developed  them  in  turn  to  their  highest 
pitch.  The  Assyrian  idea  of  the  organic 
connection  of  repeated  units  of  design  by 
linked   curves,    ending   in   spiral   volutes,  was 


il]  FOLKLORE  49 

immeasurably  improved  by  the  genius  of  the 
Greeks,  which  seized  on  elements  of  beauty 
that  had  hitherto  remained  unproductive,  and 
gave  them  not  merely  new  life,  but  measure- 
less scope. 

I  have  thought  it  well  thus  early  to  suggest 
that  the  widespread  value  attached  to  the 
spiral  formation  as  a  decorative  pattern  has 
been  very  largely  owing  to  the  fact  of  its 
origin,  and  of  its  association  with  the  lotus, 
the  symbol  of  creative  power  or  energy,  of  the 
strength  and  divinity  of  the  sun,  of  the 
sun's  birth  from  moisture,  and  of  the  many 
sacred  phenomena  of  life.  The  lotus  was  used 
for  the  first  time  in  the  decoration  of  the 
English  throne  in  Westminster  Abbey  in 
1902 ;  and  it  will  be  seen  in  later  pages  that 
modern  research  has  largely  justified  a 
symbolism  which  was  based  rather  on  faith 
than  knowledge  (see  p.  189). 

But  we  have  found  that  escape  from  danger, 
as  well  as  ascent  into  new  being,  has  been 
associated  with  the  spiral ;  and  one  of  the 
most  delightful  forms  in  which  the  idea  occurs, 
has  been  told  me  by  Mr  George  Calderon, 
whose  knowledge  of  the  folk-lore  and  magic 
of  Eastern  Europe  seems  as  inexhaustible  as  it 
is  interesting.  It  appears  that  at  the  baptism 
of  a  Lithuanian  infant  the  parents  bury  one  of 
its  little  curls  at  the  bottom  of  a  Hop-pole,  so 

D 


50  OF   SPIRALS  [chap. 

that  the  child  may  "  twine  out  of  danger  "  in 
its  lifetime,  just  as  the  spiral  tendrils  of  the 
plant  twine  upwards  to  the  light.  Another 
strange  fancy  is  the  use  to  which  the  spirally 
twisted  seed-pods  of  Helicteres  ixora  have  been 
put  by  certain  races,  who  assumed  (by  the 
"  doctrine  of  signatures  ")  that  their  peculiar, 
shape  (see  fig.  10)  would  make  them  an 
admirable  medicine  for  "  twisted  bowels,"  or 
colic.  It  was  similarly  believed 
that  the  plant  called  "  Jew's 
Ear"  was  a  good  remedy  for 
earache. 

It  is  quite  possible,  therefore, 
that  the  sinistral  spiral  for  many 
Fio.  10.         ages  had  a  deep  signification  as  a 
Helicteres  ixora     symbol,  and  that  any  specimens 

(Seed-Pod) 

in  shells  known  (for  example) 
in  the  early  sixteenth  century  would  be 
brought  home,  if  possible,  by  travellers,  and 
valued  by  collectors,  for  this  extraneous 
reason,  quite  apart  from  the  biological  prob- 
lem they  present.  The  four  great  columns 
set  up  behind  the  High  Altar  in  St  Mark's  at 
Venice,  are  all  carved  in  left-handed  spirals; 
and  some  special  value  connected  with  that 
formation  is  suggested  by  the  tradition  that 
they  originally  came  from  the  Temple  of 
Solomon  in  Jerusalem.  The  same  spiral  was 
carved    on    the    pillar    of    St    Bernwand    at 


. 





il]  SINISTRAL   SHELLS  51 

Hildesheim  in  1022.  I  think,  too,  that  any- 
one who  had  ever  studied  the  laws  of  organic 
structure  would  be  particularly  attracted  by 
shells.  The  " Allegory"  painted  by  John 
Bellini  (in  the  Academy  at  Venice),  may  well 
indicate  that  shells  were  as  full  of  legend  and 
interest  in  his  time  as  they  are  to-day,  when 
greater  knowledge  has  only  brought  the 
certainty  of  far  more  complex  causes. 

There  are  some  divergences  in  "natural" 
spirals  which  are  inexplicable  on  the  theory 
that  one  kind  is  normal  and  the  other  very 
rare.  On  the  beach  at  Felixstowe,  for 
instance,  you  may  pick  up  specimens  of  shells 
which  exhibit  dextral  and  sinistral  curves 
in  about  equal  proportions ;  but  after  a  little 
investigation  it  appears  that  all  those  with 
the  sinistral  curve  have  fallen  out  of  the  cliffs, 
and  are  in  fact  the  fossil  Fusus  antiquus  of 
the  Red  Crag  Sea;  while  modern  whelks  of 
the  same  kind  in  the  North  Sea  apparently  all 
possess  the  dextral  curve.  The  spiral  horns  of 
fossil  animals,  however,  do  not  differ  from  those 
of  living  creatures.  Near  Lake  Tanganyika 
there  is  an  amphibious  mollusc  with  a  large 
shell,  called  Lanistes,  which  in  that  locality 
always  exhibits  a  spiral  of  the  left-handed 
formation.  The  same  shell  when  it  is  found 
at  Lake  Nyassa  or  the  Victoria  Nyanza, 
exhibits   a   dextral   helix.     Is   this    difference 


52  OF  SPIRALS  [chap. 

connected  with  the  fact  that,  as  the  recent 
Biological  Expedition  seems  to  show,  Lake 
Tanganyika  has  had  some  past  connection 
with  the  ocean,  whereas  the  others  are  fresh- 
water lakes  ? 1  There  is  another  strange  beast 
within  its  waters  which  exhibits  one  kind 
of  spiral  externally,  and  another  internally, 
but  it  still  awaits  a  more  precise  examina- 
tion. 

The  development  of  microscopical  and 
photographical  research  has  put  before  our 
designers  many  beautiful  forms  in  Nature 
which  older  workmen  never  knew.  In  such 
organisms  as  Hexacoralla,  the  diatoms,  the 
calcispongise,  and  snow-crystals,  the  most 
exquisite  combinations  are  to  be  found,  which 
should  alone  be  sufficient  to  inspire  a  new 
school  of  design  in  ornament ;  and  though  I  am 
here  chiefly  concerned  rather  with  structure 
than  with  decoration,  these  examples  are  all 
germane  to  the  general  principle  of  this  Essay, 
which  aims,  in  the  humblest  manner,  at 
suggesting  a  return  to  Nature  by  our  crafts- 
men, fortified  as  they  now  are  by  the  enormous 
advances  in  scientific  knowledge  since  the 
days  when  the  old  workmen  drew  their 
inspiration  from  the  things  they  saw.  In  the 
Past,  men  worked  well  because  they  worked 

1  See  "The  Tanganyika  Problem,"  just  published  by 
J.  E,  S.  Moore.     (Hurst  &  Blackett.) 


_ 


il]  THE   GOTHIC   SPIRIT  58 

in  one  style.  Now  the  majority  of  our 
architects  copy  bits  from  every  previous  style, 
and  lose  all  originality.  The  best  style  of  the 
thirteenth  century,  for  instance,  may  be 
almost  entirely  explained  by  that  illuminating 
flash  of  light  in  which  men  saw  the  true 
proportions  of  Nature,  the  unsurpassable 
beauty  in  the  structure  of  her  forests,  the 
moulding  of  her  flowers,  the  living  grace 
of  her  animals  and  plants.  We  know  far 
more  to-day.  Will  it  not  be  worth  while 
to  try  if  we  cannot  create  something  for 
ourselves  a  little  better  ? 


CHAPTER  III 


OF    PLANTS 


As  woodbine  weds  the  plant  within  her  reach, 
Rough  elm,  or  smooth-grained  ash,  or  glossy  beech, 
In  spiral  rings  ascends  the  trunk  and  lays 
Her  golden  tassels  on  the  leafy  sprays.' ' 

TN  plants  many  particularly 
beautiful    examples    of 
spiral      formations       and 
growth  are  to  be  found, 
and   it  will    not   be   for- 
gotten in  this  connection 
that  the  structural  classi- 
fication of  plants  owes  as 
much   to   the    researches 
of  Leonardo  da  Vinci  as 
does      the      science      of 
anatomy;   and   it   is   not 
generally      known     that 
Leonardo    also    carefully 
studied     in     the     fourth 
book    of    the    "Trattato"    the     system     on 
which     leaves    are     disposed     and     arranged 
about     their     stalks,    long    before     Bonnet's 

54 


Fig.  12. 

Pine  Cone. 


Fig.  11. 

"Lady's  Tresses"  [Neottia  spiralis.) 
[To  face  page  55. 


chap,  in]  AN   ORCHID  55 

"Spiral  Theory"  (to  which  I  shall  refer  later 
on)  had  been  published  in  1754.  One  of 
his  many  beautiful  drawings  of  botanical 
subjects  from  the  Windsor  Collection  is 
reproduced  in  fig.  48.  He  was  especially 
fond  of  the  many  exquisite  spiral  lines  ex- 
hibited in  the  growth  of  the  Cyclamen. 
Since  his  day  the  subject  has  been  investi- 
gated by  many  great  observers,  and  the  mere 
facts  of  spiral  growth  would  take  too  long 
to  enumerate  here. 

A  very  peculiar  effect  is  observable  in  the 
growth  of  an  Orchid,  called  "  Lady's  Tresses  " 
{Neottia  spiralis),  found  for  me  in  North 
Devonshire.  It  is  not  a  climbing  plant  at 
all,  yet  its  buds  are  arranged  to  catch  the 
light  in  an  exquisite  spiral  of  the  rare 
sinistral  form,  which  can  almost  be  seen  to 
move  as  the  plant  stands  by  a  window  in  a 
glass  of  water.  The  drawing  in  fig.  11 
was  an  exceedingly  difficult  piece  of  work, 
so  often  did  the  plant  slightly  alter  its 
surfaces  during  the  hour  it  was  being  closely 
studied. 

In  the  cone  of  Pinus  smithiana  (fig.  12), 
the  spiral  arrangement  of  the  overlapping  leaves 
is  very  distinct.  The  economy  of  space  ensured 
at  the  points  of  growth  is  as  observable  as 
the  curious  manner  in  which  each  of  these 
leaves   is   enabled,  by  its    special   relation   to 


56 


OF  PLANTS 


[chap. 


its  neighbours,  to  obtain  the  maximum  of 
light  with  the  minimum  of  shade.  In  this 
instance,  it  should  be  noted  that  the  true 
growth  is  a  right-handed  spiral.  In  this  cone 
the  lines  of  a  left-handed  spiral  (in  which 
the  beginning  of  each  line  is  on  the  left, 
and  the  lowest  point  on  the  right)  may  also 
be  observed,  but  in  them  it  will  be  seen  that 


Wax  Palm. 


Fig.  13. 


Date  Palm. 


the  scales  are  intersected  by  other  scales  from 
the  row  above,  whereas  in  the  true  spirals 
the  scales  grow  round  and  round,  overlapping 
each  other,  but  never  interfered  with  by  a 
scale  from  a  different  line. 

In  Museum  No.  2  at  the  Royal  Botanical 
Gardens,  Kew,  is  a  section  of  the  trunk  of 
the  Carnauba  Palm  from  Brazil,  sometimes 
called  the  Wax   Palm    (Copemicia  cerifera), 


m.]  SCREW  PALMS  57 

which  shows  very  clearly  the  left-handed 
spiral  exhibited  in  the  example  of  the  same 
tree  in  the  British  Museum  of  Natural 
History,  drawn  in  fig.  13.  But  there  is 
another  example  of  this  same  Wax  Palm  in  the 
same  room  at  Kew,  which  is  no  less  clearly 
arranged  as  a  right-handed  spiral.  The  Date 
Palm  {Phoenix  dactylifera),  also  shown  in  fig. 
13,  was  drawn  from  an  example  in  the  Museum 
at  South  Kensington,  and  shows  a  right- 
handed  spiral ;  but  in  Museum  No.  3  at  Kew, 
the  same  tree  exhibits  a  left-handed  spiral. 
If  the  common  Chestnut  Tree  be  carefully 
compared  to  the  Horse  Chestnut,  it  will  be 
seen  that  the  spiral  growth  of  the  bark  on 
their  straight  stems  is  set  in  different  ways. 
Of  all  the  plants  I  examined  at  Kew,  the 
various  kinds  of  Pandanus  in  the  large  Palm 
House  afforded  the  most  beautiful  instances  of 
this  remarkable  form,  and  their  growth  is 
extraordinarily  like  that  of  a  spiral  staircase. 
But  here,  again,  we  get  the  same  puzzling 
divergencies.  Pandanus  vandermeschii,  a 
maritime  variety  of  this  "  screw-palm "  from 
Madagascar,  is  arranged  in  a  right-handed 
spiral,  as  is  Pandanus  utilis  (fig.  14).  But 
the  left-handed  spiral  is  found  both  in 
Pandanus  sylvestris,  from  the  Isle  of  Bourbon, 
and  in  Pandanus  millore,  from  the  Nicobar 
Islands.     The    plant     called    "  Rata,"    which 


m 


OF   PLANTS 


[chap. 


climbs  up  the  New  Zealand  Gum-Tree,  is  an 
example  of  another  kind  of  spiral  growth. 
A   visit  to   Kew   Gardens  will  reveal   many 


Fig.  14. 

Pandanus  utilis. 


more  instances  of  the  same  formation.  In 
the  flower  of  the  white  Water-Lily  the  various 
organs   will   be   found   to    be   arranged   in   a 


m]  CONVOLVULUS  59 

continuous  spiral,  and  the  Egyptians,  noticing 
a  similar  formation  in  the  Onion,  often  used 
that  plant  to  typify  eternity.  In  all  the 
more  primitive  flowers  a  spiral  formation  is 
exhibited,  as  opposed  to  the  concentric  circles 
in  the  "floral  diagrams"  of  more  highly 
developed  species.  This  spiral  arrangement 
also  seems  to  me  to  be  not  only  nearer  to 
primitive  Nature,  but  also  more  beautiful 
and  suggestive ;  for  the  spiral  begins  in  the 
centre  with  the  carpels,  and  the  various  organs 
in  the  course  of  their  growth  gradually  slide 
out  of  one  formation  into  another,  until  they 
become  the  sepals  on  the  outside,  which  are 
often  green  and  leaf-like. 

The  bud  of  the  Convolvulus  closes  and  opens 
with  a  spiral  twist,  and  it  may  be  noted  that 
the  Byzantine  builders  of  St  Mark's  were 
peculiarly  fond  of  the  beautiful  lines  of  the 
Water-Lily  and  the  Convolvulus  flowers,  as 
motives  for  the  decoration  of  their  columns ; 
not,  perhaps,  taking  these  forms  consciously, 
but  producing  the  same  effects  by  the  careful 
modelling  and  the  artistic  proportions  of  their 
convex  and  concave  capitals.  In  all  ordinary 
Yews  the  leaflets  grow  opposite  each  other, 
but  there  is  now  a  variety  in  which  the 
leaflets  are  set  in  a  spiral,  and  the  name 
by  which  they  are  distinguished  is  a  record 
of    the    fact    that    all    were    grown    from   a 


60  OF  PLANTS  [chap. 

single  "sport"  which  occurred  at  Florence 
Court. 

Some  very  extraordinary  spiral  fossils,  found 
in  the  Bad  lands  of  Nebraska,  have  only  just 
had  attention  drawn  to  them  by  the  scientific 
world ;  and  by  the  kindness  of  Dr  W.  H. 
Drummond,  of  Montreal,  a  specimen  will,  it 
is  hoped,  soon  be  placed  in  the  British  Museum 
at  South  Kensington.  Their  exact  origin  and 
nature  are  still  the  subject  of  discussion,  but 
as  the  balance  of  expert  opinion  inclines  to  the 
belief  that  they  are  not  only  organic,  but  also 
plants,  I  have  inserted  what  is  known  about 
them  in  the  present  chapter. 

Professor  Erwin  Hinckley  Barbour  has 
published  an  illustrated  description  of  many 
examples  of  these  "Devil's  Corkscrews"  or 
"Fossil  Twisters,"  called  in  more  scientific 
terminology,  Dcemonelix,  which  he  found  in 
large  quantities  at  Eagle  Crag,  on  Pine  Ridge, 
near  Harrison,  in  Sioux  County,  Nebraska. 
These  peculiar  structures,  as  anomalous  as 
they  are  unique,  are  found  over  an  area  of 
some  400  square  miles,  between  the  White 
River  and  the  Niobrara  River,  and  to  a  depth 
of  about  200  feet.  They  are  corkscrew-shaped 
columns  of  quartz,  sometimes  embedded  in 
sandstone,  sometimes  "weathered  out"  quite 
clear  of  the  original  matrix.  The  spiral  varies 
in  length,  but  sometimes  is  as  much  as  twenty 


in.]  D^MONELIX  61 

feet  long,  and  perfectly  regular  throughout. 
At  the  lower  end  is  a  large  transverse  attach- 
ment, not  spiral  but  smooth,  and  roughly 
cylindrical  in  shape,  as  large  round  as  a  hogs- 
head, and  longer  than  the  spiral  growth  above 
it.  The  surface  of  these  spiral  fossils  is  a 
tangle  of  ramifying,  intertwining  tubules 
about  an  eighth  of  an  inch  in  diameter,  which 
thicken  inside  into  a  solid  compact  wall 
showing  (under  the  microscope)  plant  tissue 
arranged  in  fibres.  Every  microscopic  section, 
without  exception,  shows  unmistakable  plant 
structure. 

An  immense  lake  of  fresh  water,  in  long 
distant  periods  of  time,  once  covered  the  great 
basin  east  of  the  Rocky  Mountains,  of  which 
the  sand-rock  of  the  modern  district,  all  sedi- 
mentary and  of  aqueous  origin,  is  a  relic.  In 
the  course  of  ages  this  lake  became  filled  up 
by  detritus  poured  in  from  the  rivers,  and  its 
water-plants  were  buried  in  sand.  By  degrees 
these  plants  decayed,  and,  particle  by  particle, 
were  replaced  by  silica,  the  material  of  quartz ; 
and  in  this  manner  the  huge  corkscrews  of 
quartz  now  found  on  Pine  Ridge  have  pre- 
served the  shape,  the  spiral  growth,  and  the 
huge  roots,  of  the  vast  water- weeds  which 
flourished  long  ago  at  the  bottom  of  the  lake, 
and  persisted  in  growing  at  various  levels,  one 
above  the  other,  as  the  filling-up  process  went 


62  OF   PLANTS  [chap. 

on,  until  at  last  the  lake  became  dry  land,  and 
its  weeds  vanished — to  reappear  as  Dcemonelix. 
The  spirals  are  both  right-handed  and  left- 
handed,  and  their  symmetrical  arrangement 
round  a  vertical  axis  is  alone  sufficient  proof 
that  they  are  not  the  remains  of  any  animal  or 
of  any  animal's  abode. 

Other  strange  hypotheses  have  been  put 
forward  to  explain  these  odd  formations ;  but 
this  is  not  the  place  to  enlarge  upon  them ; 
for  the  theory  that  they  are  the  fossil  stalks  of 
giant  water- weeds,  explains  all  the  facts  as 
known  at  present;  and  though  the  skeletons 
of  animals  have  in  two  cases  been  found  in 
connection  with  them,  I  cannot  believe  that 
Dcemonelix  was  ever  a  rabbit-burrow. 

The  phenomena  of  climbing  plants  are 
among  the  most  interesting  of  all  spiral 
developments  in  Nature ;  the  subject  of  their 
right-  and  left-handed  spirality  is  now  being 
investigated,  I  believe,  by  Francis  Darwin, 
who  should  produce  some  very  valuable 
results.  In  most  observed  instances,  the  Hop 
and  the  Honeysuckle  twine  to  the  left,  but  the 
majority  of  twining  plants  exhibit  a  right- 
handed  screw,  contrary  to  the  sun,  as  in  the 
case  of  the  French  Bean,  the  Convolvulus,  the 
Pea  tribe,  and  the  Passion-flower.  Charles 
Darwin  once  examined  seventeen  plants  of 
Loasa  aurantiaca,  and  found  that  eight  showed 


in.]  NUTATION  63 

the  dextral  formation,  five  preferred  the 
sinistral,  and  four  reversed  their  spiral  after 
a  part  of  their  growth  had  taken  place  in 
one  direction.  Plants  became  climbers,  he 
thought,  in  order  to  expose  their  leaf-surfaces 
to  as  much  action  of  light  and  air  as  possible, 
and  to  do  this  with  the  least  possible  ex- 
penditure of  organic  matter.  The  facts 
observable  in  their  growth  certainly  make 
it  very  difficult  to  accept  the  phrase  "the 
power  of  movement"  as  a  differentiation 
between  animals  and  plants. 

In  examining  those  plants  which  twine 
spirally  round  a  support,  Charles  Darwin 
found  that  in  two  hours  and  eight  minutes  the 
shoot  of  a  Hop  made  one  complete  revolution 
to  the  left  with  the  sun,  and  that  the  tip 
of  a  31 -inch  shoot  of  Ceropegia  Gardnerii 
made  a  circular  movement  to  the  right  at  the 
rate  of  33  inches  an  hour,  contrary  to  the 
sun,  in  search  of  an  object  round  which  to 
twine.  Every  part  of  such  a  revolving  shoot 
in  a  twining-plant  has  its  own  separate  and 
independent  movement,  described  by  Sachs 
as  "revolving  nutation,"  a  movement  which 
appears  to  be  due  to  the  more  rapid  growth  of 
cells  on  one  aspect  or  edge  than  on  the  other, 
which  makes  a  curve  in  the  shoot,  and  rotates 
it,  as  the  growth  alters  and  alternates.  The 
result  of  this  is  that  when  a  revolving  shoot 


64  OF  PLANTS  [chap. 

meets  with  a  support,  its  motion  is  arrested  at 
the  point  of  contact,  but  the  free  projecting 
part  goes  on  revolving.  As  this  continues, 
higher  and  higher  points  are  brought  into 
contact  with  the  support  and  there  arrested, 
and  thus  the  shoot  winds  round,  just  as  a 
swinging  rope  which  hits  a  stick  coils  round 
the  stick  in  the  direction  of  the  swing. 

"  Irritability "  has  nothing  therefore  to  do 
with  these  phenomena.  The  shoot  twines 
round  its  support  rather  more  slowly  than 
it  would  revolve  by  itself  (the  difference 
being  about  1^  to  1),  owing  to  the  con- 
tinued disturbance  of  force  by  arrestment  at 
various  points.  But  when  the  shoot  has  made 
its  first,  close,  firm  spiral,  it  slips  up  the 
support  in  more  open  spirals,  because  it  is  freed 
from  the  pull  of  gravity.  "  The  majority  of 
twining  plants,"  says  Dr  Wherry  (  "  On  Spiral 
Growth,"  1898),  "are  no  longer  able  to  climb 
actively,  if  their  support  forms  a  smaller  angle 
with  the  horizon  than  forty -five  degrees ;  and 
the  influence  due  to  gravitation  is  such  that  if 
the  pot  containing  a  plant  which  twines  round 
a  rod  is  inverted,  so  that  the  twining  apex  is 
lowermost,  the  youngest  coils  of  the  shoot  will 
loosen  themselves,  the  free  terminal  bud  will 
erect  itself,  and  will  again  grow  upwards  close 
to  the  rod." 

After  carefully  investigating  the  growth  of 


m.]  HOPS  65 

Hops  up  a  straight  meshed- wire  fence,  set  up 
round  a  Berkshire  tennis-lawn,  I  found  one 
example  of  the  twining  apex  having  got  lower- 
most, owing  to  some  interference  by  the 
gardener  during  the  growth  of  the  plant.  In 
the  course  of  the  next  twenty-four  hours  the 
free  terminal  bud  had  erected  itself  again, 
turned  upwards,  and  twined  to  the  left  up  its 
own  pendent  shoot,  taking  three  spiral  twists 
completely  round,  before  allowing  the  new 
extremity  to  grope  freely  in  the  air  after  a 
fresh  support.1  In  this  instance,  there  was  not 
only  the  spiral  curve  to  be  observed,  but  also  a 
very  clearly  marked  spiral  growth  in  the  fibre 
of  the  plant  itself,  which,  in  four  out  of  five 
observed  cases,  was  strongly  sinistral.  In  the 
fifth  case  it  was  nearly  straight,  but  whenever 
any  inclination  was  observable,  it  was  to  the 
right.  The  reason  for  this  exception  I  was 
not  able  to  discover.  Indeed,  the  whole 
question  of  torsions  in  the  true  axis  of  a  spiral 
twist  revealed  a  serious  complication  for  so 
unskilled  an  observer  as  myself.  Fortunately, 
however,  a  reference  to  Charles  Darwin's  ex- 
periments showed  that  the  axis  is  twisted,  in 
all  cases,  owing  to  the  roughness  of  the  usual 
natural    support,    and    the    rough,    glutinous 

1  This  hop-branch  was  the  model  for  the  conventional 
design  (by  J.  E.  Cook)  of  the  binding  on  the  back  of  this 
book. 

£ 


66  OF  PLANTS  [chap. 

surface  of  my  Hop- shoot  is  a  good  example  of 
this.  He  even  trained  some  Kidney-beans  up 
a  smooth  glass  rod,  to  prove  that  they  scarcely 
showed  any  twisting  at  all.  No  doubt  the 
twist  provides  an  additional  strengthening  of 
the  fibre,  which  enables  the  plant  to  surmount 
inequalities,  and  the  spiral  twist  (as  opposed  to 
the  spiral  curve)  in  the  horns  of  goats  and 
antelopes,  and  on  the  columella  of  certain 
shells,  may  be  an  evidence  of  a  similarly 
necessary  strengthening  process. 

A  different  class  of  climbing  plants  is  that 
which  possesses  " irritable"  organs,  such  as 
tendrils,  which  clasp  any  object  they  touch. 
These  can  grow  horizontally,  or  up  and  down, 
in  distinction  to  those  twining  plants  which 
can  only  coil  themselves  round  and  climb  up 
supports  that  are  almost  upright.  Whereas 
these  latter  always  go  round  a  stick  in  the 
direction  of  their  own  revolving  movement  of 
growth  (which  may  be  either  to  the  right  or 
the  left,  as  we  have  seen),  tendrils  can  curl 
indifferently  to  either  side,  according  to  the 
position  of  the  supporting  stick,  and  the  side 
first  touched,  the  clasping  movement  of  their 
extremity  being  undulatory  or  vermicular. 
The  tendrils  of  all  tendril-bearing  plants 
contract  spirally  after  they  have  caught  an 
object — with  about  four  exceptions,  of  which 
Smilax  aspera   is  one ;   and  this  contraction, 


iil]  BRYONY  67 

says  Charles  Darwin,  is  quite  independent  of 
that  power  of  spontaneously  revolving  which 
is  observable  (by  "  nutation "  )  in  the  apex 
both  of  the  shoot  and  the  tendril ;  for 
Ampelopsis  hederacea  does  not  thus  revolve 
at  all.  The  use  of  the  spiral  contraction  of 
a  tendril  is  to  drag  up  the  shoot  by  the 
shortest  course  towards  the  object  clasped 
without  any  waste  of  growth.  This  same 
spiral  contraction  also  makes  the  tendrils 
highly  elastic,  and  therefore  stronger  to  resist 
the  wind,  so  that  the  Bryony,  for  example, 
will  outride  a  storm  like  a  ship  with  two 
anchors  and  a  long  range  of  cable  that  serves 
as  a  spring. 

In  the  Bryony  a  filiform  organ  grows  out 
from  the  plant,  as  Dr  Wherry  observed,  and  be- 
comes "  irritable  "  in  such  a  fashion  that,  while 
revolving  at  its  free  end  exactly,  as  if  groping 
for  a  prop,  when  this  free  end  touches  a  twig, 
it  coils  round  it  at  once.  The  coiling  tendril 
then  develops  a  corkscrew  spiral  twist  in  one 
direction  in  one  part,  and  in  another  direction 
in  another  part,  with  a  short  straight  portion 
between.  This  reversal  of  the  spirals  after 
fixation  sometimes  occurs  only  once,  some- 
times as  much  as  seven  or  eight  times,  but 
the  number  of  times  it  appears  in  one 
direction  is  always  equal  to  the  number 
of   times    in   which   it    appears    in    another. 


68  OF  PLANTS  [chap. 

The  reason  for  this  is  to  be  found  in  the 
mechanical  necessity  for  preventing  excessive 
torsion.  We  have  seen  that  a  twining  plant, 
as  it  binds  its  spiral  curve  round  a  support, 
develops  a  spiral  twist  also.  This  twisting 
involves  a  twisting  of  the  axis  in  the  same 
direction,  which,  if  persisted  in  for  too  long  in 
the  same  direction,  would  ultimately  burst  the 
tendril.  But  if  just  as  many  turns  are  subse- 
quently taken  by  the  spiral  in  the  opposite 
direction,  the  strain  involved  by  the  twisting 
of  the  axis  is  removed. 

I  can  the  more  cheerfully  leave  this  part  of 
my  subject  somewhat  incomplete,  because  the 
vast  majority  of  twining  and  tendril  plants  still 
await  investigation  by  more  competent  ob- 
servers; nor  does  it  seem  possible  to  explain 
their  ways  until  we  understand  a  little  better 
how  the  forces  of  gravity  and  light  act  upon 
processes  of  growth.  In  many  instances  the 
resulting  spiral  may  have  originated  in  what 
we  should  call  "  mere  accident, "  or,  as  Darwin 
expressed  it,  in  "causes  which  are  not  ap- 
parent to  us."  But  several  of  the  problems 
presented  seem  to  go  much  deeper,  and  even 
to  touch  those  elemental  laws  which  govern 
universal  life  and  strength  and  movement,  and 
give  their  final  proportions  to  the  handiwork 
of  man. 

The    investigations    into    the     system     on 


in.]  BONNETS  THEORY  69 

which  leaves  are  arranged  upon  a  stem, 
begun  by  Leonardo  four  centuries  ago, 
have  only  just  arrived  at  something  ap- 
proaching to  an  intelligibly  philosophical  ex- 
planation. For  a  hundred  and  fifty  years,  what 
is  known  as  the  "  Spiral  Theory "  of  Bonnet, 
formed  the  foundation  of  all  studies  in 
phyllotaxis  ;  that  is  to  say,  in  the  consideration 
of  a  stem  bearing  leaves  as  an  axis  and  its 
appendages.  In  1754  Botanists  were  still 
dominated  by  the  doctrines  of  Constancy 
of  Species,  and  as  morphology  dealt  solely 
with  adult  structures,  it  arrived  at  the  very 
simple  ideal  of  a  formal  account  of  the 
framework  of  the  fully  matured  stem,  leaves, 
flowers,  and  fruit;  developmental  stages,  and 
buds,  being  considered  as  unessential.  Bonnet 
therefore  took  a  mature  stem,  and  chose  upon 
it  a  leaf  (A),  which  came  exactly  above  another 
(B).  He  then  showed  that  the  intermediate 
leaves  were  arranged  as  a  spiral,  exactly  as  if 
(B)  were  the  bottom  point  on  the  cylinder 
in  fig.  3,  and  the  intermediate  leaves  were 
arranged  along  the  string  until  they  reached 
(A)  at  the  topmost  point  of  the  cylinder.  In 
this  way  he  determined  what  is  known  as  the 
64  two-fifth  spiral,"  in  which  the  sixth  leaf  is 
inserted  exactly  over  the  first  of  a  spiral  series, 
which  makes  two  complete  revolutions  of  the 
stem.       By  the   help   of  the    mathematician 


70  OF  PLANTS  [chap. 

Calandrini,  he  formulated  a  correct  geometrical 
conception  of  a  helix,  with  parallel  screw-thread 
winding  round  the  cylindrical  stem.  This 
mathematical  conception  was  arranged  to 
fit  certain  definite  facts,  and  with  this  as  a 
basis,  Schimper  and  Braun  (1830-35)  raised 
"an  enormous  edifice  of  beautifully  precise 
nomenclature." 

But  by  degrees  appeared  the  results  of 
such  ideas  as  were  contained  in  Goethe's 
Theory  of  the  Metamorphosis  of  Leaves, 
in  Lamarck's  Researches  into  Development 
and  Heredity,  in  Von  Mohl's  Discovery 
of  the  Growing  Substance  in  Plants,  in 
Darwin's  great  Hypothesis  of  Evolution. 
By  degrees  the  type  plant  of  the  new 
morphologist  became  the  growing  body,  as 
seen  in  the  growth  of  the  members,  growth  of 
the  axes,  growth  of  the  whole  individual, 
growth  of  the  race.  But  while  critics  ex- 
claimed that  Bonnet's  mathematical  conception 
had  been  gratuitously  introduced  into  the  plant, 
and  was  "mere  playing  with  the  properties 
of  numbers,"  they  did  not  apparently  realise 
what  Bonnet  himself  thoroughly  understood, 
that,  being  ignorant  of  protoplasmic  growth, 
he  dealt  solely  with  adult  structures  which 
had  ceased  growing. 

At  last  Mr  A.  H.  Church,  a  well-known 
and   distinguished   botanist  in  Oxford,  came 


in.]  CHURCH'S  THEORY  71 

forward  with  a  new  mathematical  conception, 
founded  on  the  new  mathematical  data 
afforded  by  the  transition  of  the  morphological 
standpoint  from  that  of  adult  construction  to 
that  of  growing  systems*  As  a  starting-point 
for  such  a  conception,  Mr  Church  very 
properly  propounded  a  certain  ideal  condition. 
Just  as,  in  the  consideration  of  the  Newtonian 
laws  of  motion,  the  purely  abstract  and 
mathematical  conception  of  "  uniform  motion  " 
precedes  that  of  varying  motion,  so  the 
growth  of  a  mass  of  protoplasm  may  be 
conceived  as  a  "  uniform  growth,"  expansion 
taking  place  around  a  hypothetical  central 
point.  From  this,  Mr  Church  deduces  the 
hypothesis  that  logarithmic  spiral  curves  (see 
fig.  35),  with  the  straight  line  and  circle  as 
limiting  cases,  are  the  sole  curves  of  uniform 
growth  expansion.  Spiral  phyllotaxis  must, 
in  future,  therefore  be  based  on  a  logarithmic 
spiral  on  a  plane  surface,  and  not  on  Bonnet's 
old  idea  of  a  helix  winding  on  a  cylinder,  which 
is  merely  the  expression  of  the  attainment  of 
uniform  volume  by  members  in  a  spiral  series, 
and  which,  if  carried  on  to  a  plane  as  a  spiral 
with  equal  screw-thread,  would  become  a 
spiral  of  Archimedes. 

Of  course,  when  applied  to  the  living,  and 
admittedly  irregular,  growing  plant,  the  con- 
ception  of  a   logarithmic  spiral  would   be  as 


72  OF  PLANTS  [chap.  in. 

difficult  to  prove  by  actual  measurement  as 
was  Bonnet's  theoretical  helix.  But  now  the 
standpoint  is  changed,  it  becomes  possible  not 
only  to  deal  with  uniformly  growing  systems, 
to  deduce  mathematically  their  various  pro- 
perties, to  watch  them  (as  it  were)  grow  on 
paper,  but  also  (as  soon  as  the  properties  of 
uniform  growth  are  ascertained)  to  study  the 
possibility  of  varying  rates  of  growth,  and  to 
state  the  growth  of  an  irregular  body  in 
mathematical  terms  as  precise  as  those  which 
indicate  the  erratic  orbit  of  a  comet. 

We  shall  find  that  the  logarithmic  spiral 
occurs  again  in  connection  with  organic 
growth  in  later  pages  of  this  book,  and  I  shall 
have  occasion,1  before  the  end,  to  consider 
some  further  results  which  follow  from  Mr 
Church's  valuable  and  intricate  researches. 
For  the  present  I  must  conclude,  with  this 
brief  notice  of  them,  that  portion  of  my 
subject  which  has  to  do  more  particularly  with 
Botany. 

1  See  pages  124  and  185. 


CHAPTER  IV 

OF   SHELLS 

"  Year  after  year  beheld  the  silent  toil 
That  spread  his  lustrous  coil ; 
Still  as  the  spiral  grew. 
He  left  the  past  year's  dwelling  for  the  new, 
Stole  with  soft  step  its  shining  archway  through, 

Built  up  its  idle  door, 
Stretched  in  his  last-found  home  and  knew  the 
old  no  more.' ' 

TTERY    early    in    the    chain    of 

animal   creation   the    spiral    ar- 

£    rangement     makes    its    appear- 

J3    ance.1     The  cilia  on  the  top  of 

la 

^  1  Though  I  have  purposely  refrained, 
%  for  the  present,  from  introducing  pictures 
10  S  of  microscopical  specimens  into  this 
*"".  2  Essay,  I  must  refer  the  biological  student 
£  g  who  desires  them  to  the  magnificent 
js  illustrations  in  Dr  Friedrich  Hitter  v. 
J?  Stein's  "Der  Organismus  der  Infusions- 
|  thiere"  (fol.  Leipzig,  1867).  In  the 
a  second  Division,  he  will  find  left-handed 
§  spiral  lines  on  the  body  of  Spirostomum 
ambiguum  (Taf.  III.) ;  a  beautiful  spiral 
curve  in  the  filaments  surrounding  the 
head  of  Stentor  Polymorphous  (VI.) ;  and 
spirals  of  a  distinctly  logarithmic  character  in  Stentor 
coeruleus   (VI.),    S.   Roeselii  and    8.   igneus    (VIII. ),    and 

73 


74  OF   SHELLS  [chap. 

Vorticella  are  set  in  a  spiral,  possibly  with 
the  object  of  creating  a  vortex  in  the 
water  that  would  suck  food  towards  the 
mouth.  In  the  tube-building  worm  called 
Sabella,  the  gills  are  set  in  a  very  beautiful 
spiral,  no  doubt  with  much  the  same  effect 
of  converging  currents.  This  organism  is 
mentioned  by  Herbert  Spencer,  but  the  best 
picture  of  it  I  have  seen  is  in  the  Atlas 
to  "  Le  Regne  Animal,"  by  G.  Cuvier,  edited 
by  a  number  of  his  disciples  (Paris :  Fortin, 
Masson  et  Cie),  which  gives  a  very  beautiful 
drawing  of  Sabella  unispira  on  Plate  IV.  in 
the  section  "  Annelides."  An  instantaneous 
photographic  record  of  the  spiral  movement 
of  the  cilia  of  Vorticella  was  published  by 
E.  J.  Marey  in  "Le  Mouvement"  (Paris, 
1894),  since  translated  by  Eric  Pritchard. 

The  case  made  by  the  larvae  of  the  Caddis- 
fly  (Phryganeida)  is  beautifully  formed  by  a 
ribbon  twisted  up  into  a  right-handed  spiral. 
In  the  enlarged  drawing  of  this  in  fig.  15 
the  creature's  antennse  are  seen  protruding 
from  the  top  of  its  case.  In  some  sharks 
the   egg-capsules   show  a  spiral,   of  which   I 

S.  multiformis  (IX.).  In  the  third  Division  of  the  same 
work,  "Der  Organismus  der  Flagellaten "  (Taf.  XX.),  a 
good  example  of  right-handed  spiral  lines  on  the  body  is 
shown  in  Euglena  oxyuris  (figs.  4  and  5),  while  an  especially- 
well-marked  specimen  of  the  left-handed  spiral  is  to  be  seen 
in  Euglena  sjpirogyra  (fig.  7). 


iv.] 


VITAL  FORCES 


75 


reproduce  an  example  (of  a  dextral  helix)  in 
Cestracion  philippi  (fig.  16) ;  and  the  queer 
spiral  arrangement  of  certain  sharks'  teeth  has 
been  already  noticed  on  p.  42. 

The  spiral  of  the  cochlea  hidden  in  the  ear 
is  an  unmistakable  proof  that  the  bone 
containing  it  belongs  to  a  mammal,  and  it  is 
thus  that  ambitious  lizards  are  unmasked. 
Hermann  von  Meyer  once  accidentally  dropped 
a  skull  which  he  thought  be- 
longed to  a  lizard,  and  the  break- 
age revealed  the  cochlea,  proving 
that  the  bones  belonged  to  a 
mammal  which  was  christened 
Zeuglodon.  The  same  arrange- 
ment has  an  even  more  intimate 
connection  with  the  most  im- 
portant organ  in  the  human 
body,  for  Pettigrew  showed  that 
the  process  of  the  fibres  in  the 
ventricles  runs  in  spiral  lines 
from  the  tip  of  the  base  of  the  heart,  so 
that  the  muscular  constriction  of  the  systole 
is  of  the  nature  of  a  twist  or  screw.  There 
are,  in  fact,  certain  vital  forces  in  Nature 
which  are  invariably  expressed  in  a  spiral. 
It  has,  for  instance,  been  shown  that  the 
relation  of  the  direction  of  the  magnetic  force 
due  to  an  electric  current  to  the  direction  of 
that  current  itself  is  the  relation  involved  in 


[<<l^s 


Fig.  16. 

Capsule  of 
Shark's  Egg. 


76  OF   SHELLS  [chap. 

a  right-handed  screw.  Astronomers,  too,  are 
now  aware  that  the  spiral  nebulae,  though 
generally  discredited  when  originally  an- 
nounced by  Lord  Rosse,  were  photographed 
between  1880  and  1890,  and  usually  exhibit 
left-handed  whorls. 

Some  of  the  most  beautiful  and  interesting 
spiral  formations  in  Nature  are,  as  Leonardo 
knew,  to  be  found  in  horns,  a  pretty  pair  of 
which  (from  a  Bush-buck,  shot  in  1878)  is 
shown  in  fig.  17.  It  will  hardly  be  be- 
lieved that  in  the  year  these  were  brought 
home,  and  for  twenty  years  longer,  there 
existed  no  proper  scientific  terminology  for 
the  direction  of  the  spirals  in  horns,  found 
in  both  fossil  and  living  animals.  In  a 
pamphlet  on  "  Spiral  Growth,"  published  by 
Dr  George  Wherry  in  1898,  it  was  first 
pointed  out  that  the  horns  of  the  Koodoo 
exhibited  a  right-handed  spiral  on  the  left 
side  of  his  head,  and  a  left-handed  spiral  on 
the  right  side  of  his  head.  In  February  1901 
another  leaflet  by  the  same  writer  noticed 
that  "the  spiral  horns  of  animals,  such  as 
the  Koodoo,  are  symmetrically  arranged,  are 
right  and  left  by  certain  rules  to  which 
few  exceptions  only  are  found."  A  good 
deal  of  somewhat  nebulous  newspaper  con- 
troversy arose  on  the  subject ;  but  as  many 
statements  were  made  without  sufficient  proof, 


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iv.]  TWISTS  AND  CURVES  77 

and  many  words  were  used  without  any- 
proper  definition  of  their  meaning,  it  may- 
be as  well  for  me  to  give  a  few  facts  and 
illustrations  here  of  what  is  only  one  branch 
of  my  subject,  but  is  none  the  less  deserving 
of  far  more  extended  study  than  I  can  give  it 
in  this  place. 

Even  from  the  little  already  said  as  to  spiral 
formations  in  Nature  or  Art,  it  must  be  obvious 
that  the  word  "  spiral "  cannot  be  used  in  any 
argument  unless  it  is   carefully  qualified   and 
defined.     It  is   obvious,  for  instance,  that  no 
critical  comparisons  are  possible  between  such 
a   conical   helix   as  that  exhibited   in  fig.  26, 
and   such   a   spiral   curve   as   that    shown    in 
fig.  34.    We  might,  indeed,  compare  the  twisted 
horns   of    a   Markhor    (fig.    196)    to    such   a 
conical  helix  as  that  in  fig.  27 ;  but  the  horns 
of  the  Highland  Ram  (fig.  20a)  are  evidently 
a  different  kind  of  spiral,  which  can  better  be 
compared  to   such   a   mathematical   curve   as 
that  which   has   been   drawn   in  fig.   35.     In 
other    words,   we    must   carefully  distinguish 
between  the  spiral  twist,  about  an  axis  which 
coincides   with    that   of    the    horn;   and   the 
spiral    curve,    about    an     axis    which    would 
be  perpendicular  to  that  of   the  horn,  if  the 
horn   were   a   flat   spiral.       In   fig.    18   these 
two   different  forms  of  spiral  can  be  seen  in 
the    same    pair   of  horns.       From    C    to    D 


. 


78  OF  SHELLS  [chap. 

runs  the  spiral  twist  about  the  axis  CD. 
But  in  the  growth  of  the  horn  from  C, 
there  is  a  point  A,  up  to  which  a  curve  only 
is  apparent,  and  if  this  curve  were  produced, 
it  would  show  the  spiral  CAB,  about  the 
axis  CB. 

It  will  save  our  space  considerably,  if  we 
adopt  the  suggestion  that  horns  exhibiting 
right-handed  spirals  on  the  right  side  of  the 
head,  and  left-handed  spirals  on  the  left  side 
of  the  head,  should  be  called  "  homonymous." 
The  obvious  corollary  is  that  horns  which 
exhibit  right-handed  spirals  on  the  left  side 
of  the  head,  and  left-handed  spirals  on  the 
right  side  of  the  head,  may  be  described  as 
"  heteronomous."  Owing  to  a  lax  use  of 
words,  it  has  been  thought  that  all  wild 
animals  prefer  the  heteronomous  arrangement, 
while  all  tame  animals  show  a  homonymous 
formation.  You  may,  for  instance,  see  a  pair 
of  Elands  (Taurotragus  oryx)&t  the  present  time 
in  the  Zoological  Gardens  in  Regent's  Park. 
One  of  them  was  bred  in  South  Africa, 
the  other  in  France.  Both  of  them  show 
clearly  the  heteronomous  arrangement  which 
is  observable  in  a  Sing- sing  Water-buck  (Cobus 
unctuosus)  not  far  off  them.  So  far,  there- 
fore, they  support  the  suggestion  described 
above ;  and  as  the  animal  bred  in  France 
exhibits  a  spiral  with  a  slightly  longer  pitch, 


iv.]  EFFECT   OF  DOMESTICITY  79 

it  is  conceivable  that  this  spiral  may  straighten 
out  before  beginning  to  turn  the  other  way. 
This  would  mean  that  the  effect  of  domesticity 
upon  spiral  horns  would  be  that  the  heterono- 
mous arrangement  of  the  wild  varieties 
became  in  time  the  homonymous  arrange- 
ment suggested  as  proper  to  tame  animals. 
Such  a  result  is  not  only  based  on  an  incorrect 
use  of  language ;  it  is  also  contradicted  by  the 
facts. 

In  the  head  of  Tragelaphus  angasi,  shown  in 
fig.  18,  it  would  be  correct  to  say  that  the 
right-handed  twist  on  the  left  horn  (from  C 
to  D)  is  an  example  of  the  heteronomous 
arrangement  of  spirals  in  a  wild  animal. 
But  if  we  imagine  the  curve  CA  to  be 
continued  to  B,  we  find  that  it  would  form 
a  left-handed  spiral,  and  that,  being  on  the 
left  side,  it  would  exhibit  the  homonymous 
arrangement.  If  the  same  horn,  therefore, 
may  exhibit  a  right-handed  twist  and  a  left- 
handed  curve,  the  argument  concerning  the 
effects  of  domesticity  in  horned  animals  must 
be  limited  either  to  the  twist  or  to  the  curve 
in  dealing  with  the  same  kinds  of  animals,  and 
should  hold  good  in  both,  if  it  is  to  be  accepted 
at  all. 

Taking  the  spiral  twist  first,  we  find  it  most 
often  in  goats  and  antelopes,  and  the  most 
markedly    heteronomous    arrangement   exists 


80 


OF  SHELLS 


[chap. 


in  the  Markhor  (fig.  196)  of  which  I  have 
reproduced  a  drawing  of  the  Pir  Panjal  race 
( Capra  falconeri  cashmiriensis).  Compare 
the  horns  of  this  wild  goat  writh  those  of  the 
domesticated   Angora   (fig.    19a).      Here    we 


FlQ.  19. 

B 

khor. 

Spiral  Twist. 

A 

Angora, 

find  an  arrangement  which  is  just  as  clearly 
homonymous ;  for  the  twist  on  the  left  horn 
is  a  left-handed  twist,  and  the  curves  are 
homonymous  as  well.  So  far  then  as  the 
twist  is   concerned,  we  do  find   that  all  wild 


iv.]  HETERONOMOUS  HORNS  81 

animals  enjoy  the  heteronomous  arrangement, 
and  some  tame  animals  show  homonymous 
spirals. 

But  when  we  examine  horns  in  which 
the  prominent  feature  of  the  spiral  is  its 
curve,  as  is  the  case  with  nearly  all  sheep,  we 
find  that  no  wild  varieties  exhibit  the  heterono- 
mous formation,  for  the  homonymous  arrange- 
ment, which  is  convenient  and  necessary,  is 
common  to  both  wild  and  tame,  to 
Alaskan  Bighorn,  Argali,  and  Pamir  sheep 
(fig.  20,  c9  e,  d)  as  well  as  to  the  High- 
land and  the  Merino  Ram  (fig  20,  a,  b). 
Evidently,  when  horns  grow  in  curves, 
the  homonymous  formation  is  the  best, 
inasmuch  as  a  left  horn  which  produced  a 
right-handed  spiral  curve  would  not  only  be 
quite  useless,  either  for  offence  or  feeding,  but 
would  become  positively  dangerous  to  the 
animal  when  the  ingrowing  horn  began  to 
penetrate  its  skull,  or  even  its  back,  a 
freak  of  nature  which  has  been  observed 
to  occur  when  normal  growth  has  been 
affected  by  injury  of  the  base,  as  we  noticed 
in  the  case  of  the  elephant's  tusk  in  fig.  6. 
In  the  few  cases  in  which  the  curves  exhibit 
heteronomous  formation,  the  horn  is  pre- 
vented from  doing  harm  by  being  given 
a  twist  as  well,  which  carries  the  dangerous 
point  off  in  another   direction.     It  would   be 

F 


- 


82 


OF  SHELLS 


[chap. 


I 


W 


a 

P* 


iv.]  SOME   EXCEPTIONS  83 

interesting  if  it  could  be  established  that  this 
latter  peculiarity  was  exhibited  by  animals 
which  were  midway  between  sheep  and 
goats,  and  therefore  possessed  a  little  of  the 
peculiarities  of  both.  There  is  no  doubt  that 
a  horn  with  a  spiral  twist  would  be  stronger 
mechanically  than  either  a  plain  cone,  or  a 
spiral  curve,  as  may  be  seen  by  the  twisted 
plaits  on  the  columella  of  a  shell,  or  the 
twisted  fibre  in  a  twining  plant.  So  a  curved 
horn  may  very  possibly  develop  a  twist  as 
well,  if  strengthening  were  necessary,  and  it 
is  obvious  that  the  twisted  horns  of  goats 
and  antelopes  are  stronger  than  the  mere 
curves  usually  exhibited  in  the  horns  of  the 
less  pugnacious  sheep. 

There  is  an  exception  in  each  class  which 
has  come  under  my  observation.  The 
Abyssinian  Ibex  (Capra  walie)  has  no  spiral 
twist  whatever,  but  only  a  curve;  and  the 
Wallachian  sheep  with  its  queer  spiral  horns 
is  even  more  peculiar,  in  that  it  shows  no 
curve  whatever,  and  has  a  very  strongly 
marked  and  close  spiral  twist  like  a  corkscrew, 
of  heteronomous  formation.  This  animal  is 
found  in  Crete,  Wallachia,  Hungary,  and 
Western  Asia,  and  as  nothing  of  it  but  its 
horns  has  yet  reached  this  country,  it  is 
actually  impossible  to  say  whether  it  is  a 
sheep  or  a  goat,  for  the  presence  or  absence 


84  OF   SHELLS  [chap. 

of  certain  glands  cannot  be  established.  But 
judging  from  the  model  at  South  Kensington, 
and  from  five  photographs  in  the  possession  of 
Mr  Rowland  Ward,  I  am  inclined  to  believe 
that  these  characteristic  horns  are  due  to  a 
cross  of  Markhor  blood,  more  particularly  of  the 
Sulieman  Markhor  (Capra  falconeri  Jerdoni), 
which  has  very  closely  twisted  spiral  horns. 
But  one  of  Mr  Ward's  "Wallachian  sheep" 
seems  to  show  the  probability  of  this  cross  even 
more,  for  its  horns  exhibit  the  true  Markhor 
curve  at  the  beginning,  which  we  noticed  in 
fig.  196,  and  continue  in  a  far  more  open 
spiral  twist. 

My  last  observations  in  this  part  of  the 
subject  would  be  that  all  horns  which  show 
heteronomous  twists  also  exhibit  the  homony- 
mous curves  seen  in  fig.  18.  But  the  Situtunga 
(Tragelaphus  spekei)  shows  the  curves  above 
its  forehead  to  be  very  clearly  heteronomous, 
and  they  are  completed  in  heteronomous 
spiral  twists,  which  gives  a  shape  very  much 
like  that  of  the  conventional  lyre. 

So  far,  therefore,  as  I  have  been  able  to  go, 
it  seems  that  when  the  spiral  twist  occurs,  its 
better  formation  is  the  heteronomous  forma- 
tion, and  that  therefore  this  is  the  formation 
most  usually  found,  even  when  the  twist 
occurs  in  an  animal  which  usually  exhibits  a 
homonymous  curve.     In  the  case  of  curves,  on 


iv.]  BYPATHS  OF  RESEARCH  85 

the  other  hand,  the  homonymous  formation  is 
practically  inevitable,  and  the  heteronomous 
only  occurs  in  combination  with  a  twist.  The 
origin  of  these  two  distinct  kinds  of  spirals  in 
horns  does  not  appear  to  have  been  in- 
vestigated. The  beginning  of  the  divergence 
is  no  doubt  to  be  found  in  some  remote 
ancestral  type,  long  before  Man  exercised  any 
influence  upon  animals  whatever,  or  even 
appeared  upon  the  earth  at  all.  Since  the 
effects  of  domestication  upon  a  particular  breed 
would  take  a  very  long  time  indeed  to  make 
itself  visible  in  this  way,  I  am  inclined  to 
think  that  these  spiral  formations  are  rather 
the  accompaniments  of  a  differentiation  in 
species  than  the  result  of  any  domestication  of 
a  breed,  otherwise,  how  is  it  that  differences 
are  observed  in  the  spirals  exhibited  by  closely 
allied  animals  ?  This  study  of  horns,  which 
Leonardo  began  in  one  of  the  Manuscripts 
preserved  at  Windsor,  on  which  he  has 
sketched  a  head,  very  like  that  shown  in  fig. 
20a,  is  a  bypath  in  biological  research 1  that  will 
offer  results  as  interesting  as  an  investigation 
(for  instance)  into  the  growth  of  hair.  We  do 
not  at  present  know  why  the  growth  of  hair  in 

1  Another  bypath  of  biology  that  may  lead  us  to  the 
most  unexpected  results  is  the  investigation  by  Professor 
Poulton  and  others  into  animal  coloration.  It  appears 
that  animals  are  usually  dark  above  and  white  beneath, 


86  OF  SHELLS  [cha*. 

some  antelopes  and  in  all  African  buffaloes  is 
perfectly  normal  from  head  to  tail,  whereas  in 
other  antelopes  you  find  the  growth  reversed 
from  shoulder  to  head,  and  in  all  Indian 
buffaloes  it  is  reversed  from  tail  to  head. 
There  is  a  reason,  or  there  would  not  be  the 
difference.  And  there  is  a  reason,  too,  for  the 
spiral  formations  in  horns.  In  this  place,  I  can 
but  state  the  facts  I  have  observed,  and  leave 
to  others,  who  are  better  qualified,  the  task 
of  explanation.  I  cannot  agree  with  Dr 
Wherry's  further  suggestion  that  the  funnel 
created  by  the  spiral  curve  of  the  great  horn  of 
Ovis  nivicola  enables  the  small  ear  (placed  "at 
the  apex  of  the  hollow  cone  ")  to  distinguish 
sounds  better,  just  as  a  man  often  hears  more 
clearly  when  he  places  his  hand  behind  and 
round  his  ear.  Like  many  other  theories  of  a 
similar  nature,  this  stands  in  need  of  further 
proof  and  investigation,  though  it  is  a  good 
example  of  the  interest  that  may  be  found  in 
any  consideration  of  the  causes  or  origins  of 
spiral  growth. 

Certain  brachiopods  contain  very  beautiful 

because  this  arrangement  is  exactly  the  opposite  of  what 
happens  when  light  falls  upon  a  solid  body  which  need  not 
be  concealed.  A  normally  coloured  animal  in  its  normal 
surroundings  will,  therefore,  not  seem  to  be  solid,  and  will 
be  practically  indistinguishable  at  a  short  distance  against 
a  background  of  colour  and  pattern  similar  to  its  own. 


iv.]  ORIGIN  OV  SHELLS  87 

calcareous  spiral  arm-supports,  formed  by  a 
ribbon  of  lime,  and  attached  to  the  dorsal 
valve.  In  Zygospira  modesta  (Hudson  River 
Group),  these  spiral  cones  are  directed  inwards  ; 
in  Spirifer  mucronatus  (Devonian)  they  are 
directed  outward  and  backward,  and  formed  of 
many  whorls ;  in  Koninckina  leonhardi  (Trias) 
the  double  arm-supports  are  flat  spirals,  instead 
of  cones  set  on  their  edge,  and  are  each  com- 
posed of  two  lamellae. 

In  shells  I  have  found  the  most  exquisite 
examples  of  spirality  in  all  the  natural 
kingdom,  and  the  formation  of  spirals  by 
the  shell-fish  seems  to  be  still  in  need  of  a 
complete  scientific  explanation. 

When  an  elastic  "bendable"  substance  is 
growing  above  an  object,  and  dropping  at  its 
end,  it  might  sometimes  take  the  form  of 
a  plane  spiral.  But  if,  during  its  growth,  it  lops 
over  at  all  to  one  side,  it  usually  lops  over  to  the 
left,  the  result  of  which  (as  we  observed  in 
shavings)  is  the  usual  right-handed  spiral,  and 
shells  exhibiting  this  are  called  by  con- 
chologists  "  leiotropic,"  because  a  man  walking 
up  a  right-handed  spiral  staircase  would  be 
always  turning  to  the  left  (see  fig.  28,  and 
compare  fig.  7).  Very  rarely  they  lop  over 
to  the  right,  and  the  result  is  the  rare  left- 
handed  spiral  of  the  "  dexiotropic "  shell  (see 
fig.  8). 


88  OF  SHELLS  [chap. 

As  an  organism  of  this  kind  grows,  if  the 
new  piece  were  of  accurately  rectangular 
formation,  thus :  □,  the  result  would  be 
growth  in  a  continued  straight  line.  But  it 
never  is ;  for  the  dorsal  surface  of  a  shell-fish  is 
thin  and  ductile,  while  the  ventral  surface  is 
harder,  and  contains  muscles  which  continually 
exercise  a  certain  pull  upon  the  tissue  ;  so  that 
the  new  growth  is  usually  of  this  form :  (Z7 
As,  therefore,  the  dorsal  surface  expands  more 
easily  than  the  ventral,  while  the  creature  goes 
on  developing,  the  result  is  a  continuation  and 
emphasis  of  the  spiral  form,  thus  : 


It  is  only  necessary  to  remember  that  this 
spiral  is  growing  vertically  while  it  also  grows 
in  length,  and  you  may  add  the  pull  of  gravity 
to  the  other  forces  at  work  while  the  creature 
increases  in  bulk  and  weight,  until  the  spiral 
formation  of  the  shell-fish  becomes  a  little  more 
intelligible.  You  may  produce  the  same 
formation  by  squeezing  paint  out  of  a  tube,  or 
by  the  toy  called  "  Pharaoh's  serpents,"  which 
is  a  more  exact  parallel,  because  the  "  growth  " 
comes  from  beneath,  and  may  be  made  to 
exhibit  either  a  sinistral  or  a  dextral  formation 
(see  p.  41). 

In    considering    the    reasons   why   a    shell 


iv.]  SINISTRAL  SHELLS  89 

should  be  sinistral  rather  than  dextral,  I  must 
distinguish  between  those  sinistral  shells 
which  are  "sports/'  or  rare  exceptions  to  the 
dextral  rule  common  in  their  species,  and 
those  shells  which  are  sinistral  as  a  rule  of 
their  species.  There  is  yet  a  third  distinction, 
which  must  be  made  later. 

Turrilites  catenulatus  always  exhibits  a 
conical  sinistral  spiral.  Turrilites  costatus,  a 
fossil  gastropod,  commonly  called  the  "  screw- 
shell,"  is  found  in  the  Portland  formation 
as  a  rule.  Other  left  -  handed  species  are 
Columna  flammea,  from  Prince's  Island  in 
the  Gulf  of  Guinea;  Miratesta,  a  fresh- 
water shell  from  Celebes ;  Amphidromus 
perversus  from  Java ;  the  pond-snails  Physa 
fontinalis  in  Europe,  and  P.  heterostropha  of 
America. 

The  sinistral  form  of  Voluta  vespertilio 
(figs.  54  and  57)  is,  however,  the  exception 
to  the  rule  of  the  species,  which  is  found  on 
the  Italian  coasts  of  the  Mediterranean,  and 
an  Italian  collector  would  be  more  likely  to 
have  the  sinistral  form  of  a  common  shell 
than  its  ordinary  growth.  At  the  present 
day,  Mr  Fulton  informs  me  that  specimens 
of  the  sinistral  Buccinum  undatum,  though 
not  common,  can  be  bought  for  a  few 
shillings.  A  Billingsgate  porter  thinks  he 
has    a    rare    prize     when    he    finds    it,    and 


90  OP  SHELLS  [cha*. 

is  greatly  disappointed  when  he  discovers 
it  is  not  worth  gold.  Chrysodomus  antiquus, 
a  fossil  sinistral  whelk,  of  which  Mr  Morton 
Loder,  of  Woodbridge,  has  sent  me  an  ex- 
cellent specimen,  is  too  common  to  be  bought 
by  dealers  at  all.  The  genus  Amphidromus 
is  about  equally  divided  into  dextral  and 
sinistral  species.  But  in  cases  where  a  shell 
only  exhibits  the  sinistral  specimens  in  its 
fossil  form,  and  is  dextral  in  all  living 
examples,  I  have  been  unable  to  determine, 
as   yet,  any  reason  for  the  survival. 

The  third  distinction  to  be  made  in  this 
matter  is  in  such  cases  as  Spirialis,  Limacina, 
Meladromus,  and  Lanistes  (see  p.  51),  in 
which  the  shell  is  sinistral  but  the  animal  is 
dextral.  Here  Simroth,  Von  Thering,  and 
Pelseneer  explain  that  the  shell  is  really 
ultra-dextral ;  that  is  to  say,  the  whorls  have 
been,  as  it  were,  flattened,  as  in  Planorbis, 
then  the  spire  has  been  still  further  pushed 
downwards,  until  the  whole  is  turned  inside  out, 
becoming  sinistral  with  its  original  dextral 
animal.  The  proof  that  this  queer  process 
has  in  some  way  occurred,  is  arguable  from 
the  fact  that  every  dextral  shell  has  a  sinistral 
twist  to  the  operculum,  with  nucleus  near 
the  columella,  and  vice  versd  (see  fig.  38) ; 
but  in  "  ultra-dextral "  shells,  the  operculum 
is  sinistral,  in  spite  of  occurring  in  what  looks 


iv.]  THE  NAUTILUS  91 

like  a  sinistral  shell.  There  are  also  instances 
of  "  ultra-sinistral "  shells,  which  appear  to  be 
dextral  though  their  orifices  are  sinistral,  as 
in  the  fresh-water  Pompholyx  from  North 
America,  and  Choanomphalus  from  Lake 
Baikal.  Turbonilla  is  sinistral  in  its 
embryonic  form,  but  becomes  dextral  as 
an  adult. 

If  we  take  the  Telescopium  shown  in  fig. 
27  as  an  example  of  a  conical  spiral,  the 
Nautilus  pompilius  in  fig.  34  will  be  a  good 
instance  of  the  flat  spiral,  in  which  all  the 
whorls  are  practically  in  one  plane.  In  this 
picture,  the  little  projection  noticeable  in  each 
compartment  of  the  shell  is  the  siphuncle, 
a  membranous  tube  perforating  the  septa, 
which  Owen  thought  was  connected  with  the 
pericardium,  and  which  may  serve  to  lighten 
the  shell  by  the  passage  of  some  gas  into  its 
various  chambers.  In  the  Nautilus  it  nearly 
always  projects  backwards,  but  in  the 
Ammonites  it  nearly  always  projects  forwards. 
Among  the  Stephanoceratidae,  Crioceras  hi- 
furcatum  has  disconnected  whorls,  as  if  the 
various  coils  of  an  Ammonite  had  not 
joined  together,  and  it  looks  something  like 
a  ram's  horn,  or  a  rather  complicated 
hook.  Oncyloceras  spinigerum  is  a  fossil 
tetrabranchiate  cephalopod,  in  which  the 
whorls     are     also     disconnected.      Siliquaria 


92  OF  SHELLS  [chap. 

anguina  has  a  shell  that  begins  in  a  close 
spiral  and  ends  in  irregular  separated  coils. 
Cylindrella,  the  cylinder- snail  of  the  West 
India  islands,  a  palmonate  gastropod  of  spiral 
form,  has  the  last  whorl  detached  from  the 
rest,  with  a  circular  mouth-opening. 

In  the  British  Museum  of  South  Kensington, 
there  are  very  fine  examples  of  Macroscaphites 
gigas,  and  Macroscaphites  ivanii,  which  look 
like  Ammonites  beginning  to  unroll  themselves ; 
and  if  the  logarithmic  curve  in  fig.  35  be 
taken  as  the  expression  of  "  uniform  growth  " 
in  all  organic  matter,  as  Mr  Church  suggests 
it  may  be  used  in  plant-protoplasm,  it  may  be 
conceived  as  possible  that  as  the  surviving 
Nautilus  (fig.  34)  differs  from  it  in  taking  a 
wider  sweep,  while  the  fossil  Ammonite  differs 
in  exhibiting  a  tighter  spiral,  so  the  form  of 
Macroscaphites  may  represent  the  tendency  of 
a  creature  more  recent  than  the  Ammonite  to 
expand  its  coil,  and  get  a  larger  space  for  the 
life  and  growth  of  the  animal  it  shelters. 

The  position  of  the  siphuncle  may  also  have 
some  connection  with  the  causes  of  survival, 
for  while  it  is  on  the  convex  side  of  Goniatites, 
and  on  the  concave  side  of  Clymenia,  it  is 
placed  in  the  middle  in  the  Nautilus.  In 
"  Les  Enchainements  du  Monde  Animal  dans 
les  Temps  Geologiques"  (Paris  1883),  M. 
Albert  Gaudry  shows  that  Orthoceras  (with  its 


iv.]  THE   SIPHUNCLE  93 

siphuncle  in  the  middle)  is  in  fact,  as  Barrande 
thought,  "  a  straight  Nautilus/5  and  the  inter- 
mediate steps  in  development  may  be  traced 
through  Aploceras,  which  shows  a  slight  curva- 
ture to  the  right  at  the  thin  end,  and  Nautil- 
oceras,  a  hook-like  formation  with  disconnected 
whorls.  In  the  same  way  M.  Gaudry  suggests 
that  Melia  (with  its  siphuncle  on  the  right  side) 
becomes  Cyrtoceras  when  the  tip  shows  a 
slight  curvature,  and  so  may  be  supposed  to 
pass  through  such  forms  as  Gyroceras  and 
Ophidioceras  to  the  Ammonite. 


CHAPTER  V 

COMPARISONS 

"  Small  and  pure  as  a  pearl.  .  . 
Frail  but  a  work  divine 
Made  so  fairily  well 
With  delicate  spire  and  whorl.  .  . 
A  miracle  of  design." 

TN  such  a  shell  as  Solarium  maximum 
■*■  (fig.  2,  a,  b)9  the  simpler  form  of  spiral 
arrangement  is  prettily  exemplified,  and  it 
is  so  easy  to  imagine  walking  in  at  the  mouth 
(or  entrance),  and  continually  turning  to  the 
left  until  the  top  is  reached,  that  this  shell 
has  been  commonly  called  the  "staircase 
shell." 

A  connection  between  shells  and  spiral 
staircases,  in  the  minds  of  those  who  were 
responsible  for  scientific  terminology  as  it  is 
now  accepted,  has  been  already  indicated  in 
the  words  "  leiotropic  "^  and  ' '  dexiotropic," 
which  are  otherwise  inexplicably  the  reverse 
of  the   spirals   they  describe.     But  it  is  still 

94 




II 


Fig.  21. 

Spiral  Staircase,  Palazzo  Contarini,  Venice. 


[To  face  page  95, 


CHAP.  V.] 


SCALA   DEL   BOVOLO 


95 


further  suggested  by  the  nomenclature  of 
some  well-known  architectural  treasures  in 
Italy.  At  Fiesole,  for  example,  in  the 
convent  of  San  Domenico,  there  is  a  flight 
of  eight  steps  (leading  down  to  the  cloister) 
which  is  so  exquisitely  arranged  in  the  form  of 
a  shell  that  the  little  building  is  called  the 
"Scala  della  Conchiglia."  At 
Venice  a  more  famous  example 
may  be  found  [in  the  Palazzo 
Contarini,  near  the  "  Congre- 
gazione  di  Carita"  (No.  4299), 
which  is  reached  through  the  (J 
Calle  della  Vida  out  of  the 
Campo  Manin.  Its  shape  has 
earned  it  the  name  of  the 
Scala  del  Bovolo  (fig.  21),  and 
I  am  tempted  to  think  that  the 
architect  of  this  dextral  helix, 
with  its  exquisite  rising  spiral  of  light 
archways,  may  have  seen  the  shell  so  aptly 
called  Scalaria  scalaris  (fig.  22),  which 
exhibits  exactly  the  same  formation.  In 
this  shell  the  mouth  or  entrance  has 
gradually  grown  round  and  round  with  the 
growth  of  the  inhabitant,  leaving  a  little 
colonnette  behind  it  as  it  moved,  until  it 
reached  the  place  which  is  equivalent  to  the 
door  in  the  staircase  to  which  I  compare  the 
shell.     How    infinitely    more     beautiful     the 


Fig.  22. 

Scalaria  scalaris. 


96  COMPARISONS  [chap. 

spiral  formation  of  ascending  curves  in  the 
Scala  del  Bovolo  is  than  a  mere  system  of 
super-imposed  circles  (even  when  arches  and 
colonnettes  are  similarly  added)  may  be  seen 
from  a  comparison  of  the  whole  height  of 
this  staircase  (fig.  23)  with  the  Campanile  at 
Pisa  (fig.  24).  But  the  spiral  formation  itself 
is  not  invariably  a  happy  thought  in  every 
architectural  position.  Some  such  idea  of 
growth,  of  support,  of  strength,  as  is  shown 
in  the  "  Prentice's  Pillar,"  seems  as  essential 
to  it  in  Art  as  in  Nature.  The  staircase  of 
the  Rundthor  at  Copenhagen,  is,  for  instance, 
a  far  more  satisfactory  example  than  the 
twisted  copper  spire  in  the  same  locality;  or 
than  the  corkscrew- shaped  spire  of  Gelnhausen, 
near  Frankfort  on  the  Main;  or  than  the 
stone  spirals  in  one  of  the  small  steeples  of 
the  Palais  de  Justice  at  Rouen,  near  the  Rue 
Jeanne  d'Arc.1  Mere  imitation  of  externals 
without  structural  necessity,  is,  in  fact,  as 
barren  here  as  it  must  ever  be.  Perhaps 
this   is  why  I  can  never   admire  the  twisted 

1  I  am  informed  that  the  twisted  spire  at  Chesterfield, 
which  is  made  of  a  timber  frame  covered  with  metal,  was 
not  originally  constructed  in  this  screw-like  form,  but  has 
been  twisted  into  its  present  shape  by  the  decay  and 
partial  failure  of  some  timbers,  an  accidental  origin  for  an 
architectural  form  which  must  carefully  be  distinguished 
from  a  structural  shape  intentionally  created  from  the 
first, 


Fig.    23. 

Scala  del  Bovolo,  Palazzo  Contarirr, 
Venice. 


Fig.    24. 

The  Tower  of  Pisa. 

[To  face  page  96. 


Fig.  25. 

Escalier  de  la  Reine  Berthe,  Chartres. 


[To  face  page  97. 


v.] 


CHARTRES    STAIRCASE 


97 


chimneys  so  often  seen  in  Tudor  buildings,  or 
even  such  fine  sinistral  spirals  of  brickwork  as 
are  to  be  seen  in  the  chimneys  at  Framling- 
ham  Castle.  Even  when  in  its  right  place, 
in  a  staircase,  the  spiral  needs  clever  hand- 
ling if  it  is  to  be  effective, 
as  may  be  seen  in  the 
clumsiness  of  the  brickwork 
in  the  house  of  Tristan 
l'Hermite  at  Tours,  and  the 
ambitious  failure  of  the 
clustered  sinistral  spiral  in 
the  stone  stairway  of  the 
cloisters  in  the  same  town. 
In  each  case  the  steps,  too, 
are  straight  and  inartistic. 

An  even  more  delightful 
example  of  the  close  con- 
nection between  a  good 
architect's  plans  and  the 
exquisite  lines  of  Nature  is 
to  be  found  in  the  stairway 
called  "  Escalier  de  la  Reine 
Berthe"  at  Chartres  (fig. 
25).  It  exhibits  the  delicate 
exterior  ascending  dextral  helix,  and  even 
the  top  of  Mitra  papalis  (fig.  26)  with 
extraordinary  faithfulness,  and  the  parallel 
becomes  even  more  complete  when  the 
position    of   the    darkened   doorway   is   com- 

G 


Fig.    26. 

Mitra  papalis. 


98 


COMPARISONS 


[chap. 


pared  to  that  of  the  shadowy  orifice   of  the 
shell. 

In   Mitra  papalis  at  this  orifice,  you  will 
observe     the     beginnings     of   three    internal 
spiral  lines   which   suggest   that  the  internal 
arrangements  of  a  shell  have  as  much  to  teach 
us  as  its  exterior  forms ;  and  a  very  beautiful 
spiral  may  be  seen  by  the  aid  of 
the  X-rays  continuing  through- 
out   the    whole   length   of    the 
long-pointed  shells   so   common 
in  the  south.     The  clue  is  worth 
following     up,     and    a     section 
cut    through    such    a    shell    as 
Telescopium  telescopium  (fig.  27) 
actually    reveals    an   exquisitely 
firm  and  elegant  single  spiral  (a 
dextral   helix)    rising  round  the 
columella,     that      pillar     which 
supports  the  whole ;  and  this  at 
once  reminds  me  of  the  spiral 
in   a   staircase   built   in   the   old   part  of  the 
Chateau  of  Blois  many  years  before  Leonardo 
was  in  France  (fig.  28).     But  I  do  not  for  a 
moment  suggest  that  there  was  any  conscious 
comparison   in    the    mind    of   the    fifteenth- 
century  architect,  and  this  for  the  very  good 
reason  that  the  curve  of  his  stairway  and  the 
beautiful  spiral  rail  (on  which  the  left  hand 
would     rest     as     one     ascended)     are     both 


Fig.  27. 

TeUscopium 
telescopium. 


Fig.  28. 

Staircase  in  the  Old  Wing  of  the  Castle  of  Blois.  [To  face  page  J 


v.]  NATURE    AND  ART  99 

susceptible  of  a  simple  architectural  explana- 
tion; so  that  all  I  should  be  inclined  to  say 
of  this  comparison  at  present  is  that,  as  the 
lines  of  the  architecture  are  right,  and  fulfil 
their  purpose  exactly,  with  an  economy  of 
space  and  strength,  and  a  sufficiency  of 
support,  they  were  therefore  very  likely  to  be 
in  harmony  with  those  lines  which  Nature, 
the  best  of  all  artificers,  has  developed  in  her 
shell.  I  should  need  more  resemblances  than 
this  to  be  satisfied  that  one  might  have  been 
taken  from  the  other ;  but,  on  the  other  hand, 
I  shall  by  no  means  reject  such  a  possibility, 
at  the  outset,  as  absurd ;  for  architecture  is 
full  of  such  copies  from  Nature,  as  every 
organically  beautiful,  constructive  art  must  be, 
and  it  is  full  of  equally  suggestive  relics  of 
the  simpler  forms  of  shelter  from  which  the 
palace  slowly  grew.  If  the  Egyptian  pillar 
is  a  copy  of  the  lotus-plant,  so  the  peculiar 
shape  of  the  Moorish  and  Saracen  arch  is  a 
survival  of  that  wind-blown  tent,  with  conical 
top  and  bagging  sides  pegged  closely  in,  which 
was  the  habitation  of  the  Bedouin. 


CHAPTER   VI 

A   VANISHED   ART 

"  Qual  pare  a  riguardar  la  Carisenda 
Sotto  1  chinato,  quand  un  nuvol  vada 
Sovr'  essa  si  ched  ella  incontro  penda  : 
Tal  parve  Anteo  a  me.  ..." 

— Dante. 

]^TO  one  who  looks  with  a  seeing  eye  at  the 

finest  of  the  buildings  which  Leonardo 

da  Vinci  might  have  known,  can  fail  to  detect 

an  intense  perception  of  that  difference  in  detail 

and  harmony  in  relation  to  quantities  of  which 

Nature  is  the  great  exemplar.     The  "  straight 

lines"  of  the  Parthenon  are  in  reality  subtle 

curves,  and  recent  investigation  has  detected 

a  similar  delicacy  of  constructive  measurement 

in  the  great  Gothic  cathedrals.     The  influence 

of  the  study  of  flowers  and  leaves  is  especially 

marked  when  the  positions  and  proportions  of 

the  best  Byzantine  arches  ar£  examined  in  the 

light  of  the  laws  which  govern  growth.     How 

slight  and  exquisite  were  the  details  on  which 

such  laws  depended  no  one  could  realise  better 

100 


chap,  vi.]  LOST  PRINCIPLES  101 

than  the  painter  who  had  studied  the  render- 
ing of  expression  on  a  human  countenance  by 
lines  so  delicate  that  the  reason  for  the  effect 
produced  was  only  visible  to  the  few  who 
knew.  The  eye  is  even  more  influenced  by 
things  which  are  usually  "unseen"  than  by 
things  which  are  "  obvious  " ;  and  it  is  of  the 
essence  of  Beauty  that  her  origin  and  cause 
are  hidden  from  those  unworthy  to  appreciate 
her. 

Some  of  these  origins  and  causes  it  may  be 
well  to  state  here,  for  though  they  have  been 
emphasised  by  such  acute  artistic  intellects 
as  Professor  William  Goodyear  and  Mr  Julian 
Moore,  and  though  the  first  announcement 
of  their  existence  was  made  many  years  ago, 
yet  they  have  never  been  properly  appreciated 
by  a  public  which  must,  after  all,  be  the 
ultimate  arbiter  of  architectural  taste,  and 
they  are  closely  connected  with  those  methods 
of  Leonardo  with  which  we  are  now  chiefly 
interested. 

The  history  of  architectural  theory  has  seen 
a  renaissance  of  the  ideals  called  classical,  and 
a  revival  of  the  school  known  as  "  Gothic,"  of 
which  the  former  was  incomparably  the  more 
valuable,  because  the  conditions  of  society 
which  made  "the  pointed  style"  possible  in 
England,  and  gave  birth  to  the  "  Gothic " 
school  in  the  He  de  France,  could  never  re- 


102  A   VANISHED   ART  [chap. 

appear,  and  were  an  essential  concomitant  of 
the  architecture  which  expressed  them.  Yet 
an  omission  of  equal  value  was  made  by  the 
revivalists  of  both  schools.  The  real  "  Gothic  " 
preserved  certain  delicate  principles  of  con- 
structive asymmetry,  in  the  curves  and 
irregularities  in  the  masonry  of  the  old  Greek 
builders,  but  the  "Renaissance"  which 
pretended  to  go  back  to  ancient  Greek  and 
Roman  ideals,  did  not  appreciate,  even  if  it  saw, 
these  slight  divergencies  from  the  rule  of 
thumb  which  were  invisible  to  any  but  the 
trained  observer.  In  the  same  way,  the 
Gothic  Revival,  which  attempted  im- 
possibilities by  overlooking  entirely  the  radical 
changes  which  had  occurred  in  contemporary 
life,  was  fated  still  more  fully  to  destruction  by 
its  complete  ignorance  of  the  finer  subtleties 
of  mediaeval  art.  We  have  no  actual  proof  of 
this  lack  of  appreciation  in  each  case,  except 
the  proof  provided  by  the  buildings  which 
were  themselves  the  products  of  these  separate 
revivals.  For,  apart  from  Vitruvius  and  from 
the  invaluable  Note-book  of  the  architect 
Wilars  de  Honecort  (1250),  we  have  no  real 
contemporary  record  of  the  growth  of 
architectural  principles  until  these  theories 
concerning  slight  divergence  had  been  wholly 
lost.  Even  the  sentence  in  Vitruvius,  which 
seems  directly  to   refer  to   them,   was  never 


vi.]  BAD   WORKMANSHIP  103 

understood  until  the  nineteenth  century,  and 
then  only  by  the  merest  chance  on  the  part  of  an 
observer  whose  real  work  was  never  recognised. 
These  constructive  refinements,  however,  died 
out,  not  merely  because  no  record  existed 
of  them,  but  for  the  far  more  vital  reason  that 
the  public  eye  was  no  longer  delicate  enough 
to  appreciate  them,  though,  as  a  matter  of  fact, 
they  are  the  real  cause  of  beauty  in  the  finest 
of  our  old  surviving  buildings,  which  owe  their 
charm  not  merely  to  the  kindly  hand  of  time 
but  to  the  deep-laid  skill  of  their  builders. 
When  constructions  have  arisen  which  were 
designed  without  that  skill,  even  when  they 
are  supposed  to  be  exact  copies  of  the  old 
originals,  no  lapse  of  time  can  ever  lend  them 
a  beauty  which  is  no  concern  of  theirs,  as 
may  easily  be  seen  in  many  smoke-begrimed 
atrocities  of  modern  London. 

In  these  days,  division  of  labour  has  lowered 
the  capacity  of  the  individual  artisan;  and 
machine-made  work,  accustoming  the  eye  to 
inartistic  uniformity  of  ornamental  detail,  has 
also  destroyed  its  grasp  of  delicate  structural 
effects.  In  the  old  cathedrals,  the  mason  and 
the  architect,  the  artist  and  the  artisan,  were 
one.  By  the  fifteenth  century  a  Florentine, 
Leon  Battista  Alberti,  had  separated  the 
architect  from  the  builder.  In  England,  it 
was  Inigo  Jones  who  first  invariably  insisted 


104  A   VANISHED   ART  [chap. 

that  his  wood  and  stone  workers  should  copy 
his  designs  instead  of  following  their  own 
fancies.  Each  was  a  great  man,  yet  each  was 
the  unconscious  origin  of  a  great  evil  which 
has  befallen  the  art  they  loved. 

The  history  of  the  discovery  of  curves  in 
ancient  Greek,  even  in  Egyptian,  architecture, 
is  romantic  and  interesting  enough.  Every  one 
had  read  the  passage  which  suggests  them  in 
Vitruvius  since  1500.  Stuart  and  Revett  had 
measured  the  Parthenon  in  1756.  Lord 
Elgin's  workmen  noticed  nothing.  In  1810 
Cokerell  had  established  the  fact  of  entasis, 
and  in  1829  Donaldson  saw  the  lean  of  the 
columns.  But  in  1812  the  translation  of  Vit- 
ruvius, by  Wilkins,  only  contained  a  note  that 
"  this  great  refinement  ....  does  not  appear 
to  have  entered  into  the  execution  of  the  work 
of  the  ancients."  Apparently  it  never  occurred 
to  the  translator  that  it  was  worth  while  measur- 
ing "  the  work  of  the  ancients/'  before  making 
general  statements  about  it.  At  last,  in  1833, 
Mr  John  Pennethorne  discovered  the  un- 
doubted existence  of  convex  constructive 
curves  in  the  architraves  of  the  second  court  of 
the  Theban  Temple  of  Medinet  Habou.  Four 
years  afterwards  he  stood  before  the  Parthenon, 
with  the  passage  from  Vitruvius  in  his  mind, 
and  saw  those  delicate  irregularities  which  had 
remained  invisible  throughout  the  passage  of 


vl]  THE   PARTHENON  105 

so  many  unintelligent  years.  About  the  same 
time  two  German  architects,  Hofer  and 
Schaubert,  saw  them  too,  and  published  their 
discovery  in  the  "  Wiener  Bauzeitung  "  of  1838. 
Save  in  a  private  pamphlet,  Pennethorne  gave 
nothing  to  the  world  till  1878,  although  in 
1851  Francis  Cranmer  Penrose,  helped  by  the 
Dilettante  Society,  published  the  results  of  his 
measurements  of  the  Parthenon  in  "  Principles 
of  Athenian  Architecture." 

Penrose  showed  that  in  this  building  no 
two  neighbouring  capitals  correspond  in  size, 
diameters  of  columns  are  unequal,  inter- 
columnar  spaces  are  irregular,  the  metope 
spaces  are  of  varying  width,  none  of  the 
apparently  vertical  lines  are  true  perpendiculars, 
the  columns  all  lean  towards  the  centre  of  the 
building,  as  do  the  side  walls,  the  antae  at  the 
angles  lean  forward,  the  architrave  and  frieze 
lean  backward,  the  main  horizontal  lines  of 
construction  are  in  curves  which  rise  in  vertical 
planes  to  the  centre  of  each  side,  and  these 
curves  do  not  form  parallels.  Professor 
Goodyear,  who  completed  the  investigations  of 
Pennethorne  at  Medinet  Habou,  found  that 
similar  curves  existed  in  the  Maison  Carree, 
and  it  is  clear  that  while  irregularities  which 
would  be  easily  detected  or  obtrusively  con- 
spicuous were  avoided,  there  was  also  an 
unquestionable    intention    of    avoiding   exact 


106  A   VANISHED   ART  [chap. 

ratios  or  mathematical  correspondences  wher- 
ever such  an  avoidance  was  calculated  to 
produce  a  certain  effect.  That  these  devia- 
tions were  not  the  result  of  error  in  the  work- 
men, or  of  accidents  in  the  lapse  of  centuries, 
is  also  clear  from  Penrose's  calculation  that 
the  maximum  deviation  of  the  Parthenon  in 
the  case  of  lines  intended  to  correspond  (as  at 
the  two  ends)  is  as  little  as  the  fiftieth  part  of 
an  inch,  while  the  refinement  of  jointing  in  the 
masonry  is  so  great  that  the  stones  composing 
the  great  steps  have  actually  grown  together 
beneath  the  pressure  of  the  columns  they 
support.  It  is  in  fact  impossible  to  explain 
such  asymmetries  as  these,  on  the  theory  of 
faulty  work,  of  the  use  of  varying  materials 
from  different  sources,  or  of  subsequent 
accidents,  and  the  principles  thus  found  to 
be  practised  by  the  builders  of  the  Parthenon, 
have  also  been  discovered  by  Professor 
Goodyear  to  exist  not  merely  in  Egyptian, 
Greek,  and  Roman  buildings,  but  in  Italo- 
Byzantine,  Byzantine-Romanesque,  and  Gothic 
buildings,  especially  where  Byzantine  influence 
has  been  strong,  in  obedience  to  laws  which 
fell  into  abeyance  almost  completely  when  the 
classical  Renaissance  fully  established  itself. 

Oblique  plans  are  common  in  old  churches, 
and  can  easily  be  seen  in  such  examples  as  St 
Ouen  at  Rouen,  or  the  choir  arch  in  the  parish 


vi.]  OLD  ST  PAUL'S  107 

church  of  Wantage,  where  the  deflection  of 
the  building  has  been  said  to  represent  the 
position  of  Christ's  head  upon  the  cross. 
These  instances,  however,  are  of  a  grosser 
nature  than  the  curves  in  constructional  line, 
which  I  wish  chiefly  to  emphasise,  and  which 
may  be  seen  in  the  walls  of  the  nave  of 
Westminster  Abbey.  These  are  bent  inwards 
at  about  the  height  of  the  keystones  of  the 
arches,  and  outwards  above  and  below  this 
point,  as  Mr  Julian  Moore  has  shown.  They 
are  not  only  structurally  sound  to  this  day, 
but  have  retained  a  greater  beauty  than  exists 
in  any  of  the  numerous  ruler-made  copies  in 
different  modern  churches  of  the  country.  In 
Evelyn's  "  Diary  "  there  is  a  most  interesting  in- 
dication of  similar  divergencies  in  Old  St  Paul's. 
"Finding,"  he  writes  on  27th  July  1665,  "the 
main  building  to  recede  outwards,  it  was  the 
opinion  of  Mr  Chichly  and  Mr  Prat  that  it 
had  been  so  built  ah  origine  for  an  effect  in 
perspective,  in  regard  of  the  height ;  but  I  was, 
with  Dr  Wren  [Sir  Christopher]  quite  of 
another  judgement,  and  so  we  entered  it ;  we 
plumbed  the  uprights  in  several  places." 

This  implies  that  two  English  architects  of 
the  seventeenth  century  asserted  a  constructive 
existence  and  an  optical  purpose  for  an  out- 
ward divergence  from  the  perpendicular  in  the 
vertical     lines     of    the     nave     of    a    Gothic 


108  A   VANISHED   ART  [chap. 

cathedral,  and  favoured  the  preservation  of 
the  Gothic  building  as  far  as  possible.  To 
Evelyn  and  Wren,  however,  the  champions  of 
the  Renaissance,  the  old  church  was  "  only 
Gothic."  Keen  as  they  were,  they  had  lost 
something  which  two  lesser  men  remembered. 
Similar  divergencies  in  St  Mark's  at  Venice 
have  been  equally  overlooked  by  almost  every 
visitor.  The  piers  and  upper  walls  of  the  nave 
lean  outward  to  an  extent  of  18  inches  out 
of  the  perpendicular  on  each  side,  a  devia- 
tion which,  had  it  been  accidental,  or  later 
than  the  original  construction,  would  have 
disintegrated  the  arches  supporting  the  dome, 
ruined  the  frescoes,  and  destroyed  the  building. 
Again,  in  the  choir  of  Sant'  Ambrogio  at  Milan, 
the  main  piers  on  the  right  and  left  lean  out 
nearly  6  inches  from  the  perpendicular  on 
each  side ;  and  a  similar  lean  may  be  observed 
in  S.  Maria  della  Pieve  at  Arezzo,  where  the 
queer  bent  column  in  the  choir  gallery  is 
a  conspicuous  instance  of  the  capricious  and 
eccentric  forms  occasionally  developed  by  the 
hatred  of  mathematical  exactness. 

A  much  more  daring  and  aggressive  instance 
of  divergence  from  accurate  measurements  is  to 
be  found  in  the  Campanile  of  Pisa  Cathe- 
dral, which  I  reproduced  in  fig.  24.  This 
astonishing  structure  is  179  feet  in  height,  and 
is   no   less   than   13  feet  out   of  the   perpen- 


vl]  SYMMETROPHOBIA  109 

dicular,  a  peculiarity  which  has  given  it  the 
name  of  the  Leaning  Tower  of  Pisa.  This 
lean  is  more  accentuated  in  the  three  lowest 
storeys,  and  above  the  third  storey  there  is  a 
deliberate  effort  to  return  towards  the  per- 
pendicular by  means  of  a  delicate  series  of 
changes  in  the  pitch  of  the  columns  on  the 
lower  side,  and  by  a  slight  rise  in  height  of 
the  galleries  on  the  same  side.  The  reasons 
for  this  have  been  somewhat  too  hastily  and 
generally  taken  from  Vasari's  explanation  in 
the  "  Lives,"  who  attributes  it  to  inexperience 
of  the  peculiar  soil  of  Pisa  on  the  part  of  the 
architects  Guglielmo  and  Bonanno.  They 
endeavoured,  he  asserts,  to  rectify  the  settle- 
ment of  the  foundations  (which  occurred,  on 
this  theory,  just  when  the  third  storey  had 
been  completed)  by  endeavouring  to  build 
back  again  to  the  perpendicular  in  1174. 

I  cannot  accept  Vasari's  explanation  now 
that  Professor  Goodyear's  researches  into 
what  may  be  called  "  symmetrophobia "  have 
been  published.  Vasari  wrote  some  four 
hundred  years  after  the  Campanile  had  been 
built,  some  time  after  the  Italian  Renaissance 
had  cast  its  scorn  on  what  was  "  only  Gothic," 
and  in  days  when  the  marriage  of  a  daughter 
of  the  Duke  of  Tuscany  was  celebrated  by 
whitewashing  the  Gothic  frescoes  of  the 
Duomo    at    Florence.     Even    if    we    accept 


110  A   VANISHED   ART  [chap. 

Vasari's  theory  as  to  the  Campanile  alone,  it 
will  not  explain  why  similar  divergencies  occur 
in  contemporary  buildings.  The  Baptistery 
of  the  Cathedral,  begun  in  1173,  also  leans 
17  inches  out  of  the  perpendicular,  and  the 
plinth-blocks  of  its  foundations  tilt  down 
evenly  and  gradually  for  exactly  9  inches  in 
the  direction  of  this  lean.  The  Campanile 
of  S.  Nicolo  (built  by  Nicolo  Pisano)  leans 
forward  in  the  same  way,  and  also  curves 
back  again  towards  the  perpendicular.  The 
facades  of  the  Cathedral  of  Pisa,  and  of  its 
choir,  both  show  a  similar  forward  lean  in 
their  original  construction,  curving  back  again 
to  the  perpendicular. 

Its  Campanile,  in  fact,  is  not  the  result  of 
accident.  It  was  originally  built  as  it  may 
now  be  seen,  the  most  remarkable  combination 
of  Greco-Byzantine  subtlety  with  mediaeval 
exaltation  in  the  age  which  enjoyed  such  tours 
de  force  as  the  bent  column  of  Arezzo,  or 
the  Torre  del  Pubblico  of  Ravenna,  or  the 
Garisenda  Tower  at  Bologna,  which  is  163 
feet  high  and  10  feet  out  of  the  perpendicular. 
Goethe,  whose  Essay  on  Strassburg  Cathedral 
(about  1773)  was  a  veritable  re-discovery  of 
mediaeval  principles  of  beauty,  explained  this 
leaning  tower  as  intentionally  so  built  as  to 
attract  the  spectator's  attention  from  the 
numerous    ordinary    straight     shafts ;     which 


vl]  DELIBERATE   ERROR  111 

may  well  be  true,  if  we  are  to  believe 
Benjamin  of  Tudela's  statement  to  the  effect 
that  there  were  ten  thousand  towers  in  Pisa 
alone. 

I  cannot  here  commend  the  Campanile  of 
Pisa  for  its  eccentric  leaning  construction  any 
more  than  for  its  superimposed  circles  (fig.  24), 
which  lose  much  of  their  effect  by  the  equality 
of  their  vertical  divisions,  but  I  quote  it  as 
the  most  intelligible  instance  I  know  of  the 
deliberate  avoidance  of  accuracy  in  construc- 
tion for  deliberate  reasons.  It  is  exaggerated, 
and  therefore  fails  where  the  more  delicate 
effects  of  the  Parthenon  succeed;  but  its 
very  conspicuous  qualities  give  a  very  clear 
example  of  that  intentional  mystification  by 
which  the  old  builders  strove  to  get  a  look  of 
life,  of  that  nature  which  never  grows  by  rule, 
of  those  principles  of  growth  which  have 
brought  Nautilus  pompilius  so  near  to  the 
logarithmic  spiral  (figs.  34,  35)  without  exactly 
reproducing  the  mathematical  curve  (see  p.  185). 

Ruskin  noticed  some  such  divergencies 
from  accurate  measurement  in  the  old  Gothic 
buildings  of  Venice,  but  apparently  without 
appreciating  the  value  of  Penrose's  work  on 
the    Parthenon.1     Yet    the    principles    which 

1  He  emphasizes,  for  instance,  the  fact  that  the  two 
Eastern  windows  in  the  fa£ade  of  the  Ducal  Palace,  which 
overlooks  the  Riva  de'  Schiavoni,  are  lower  than  the  other 


112  A  VANISHED  ART  [chap. 

guided  the  Greek  builders  seem  to  have  lasted 
just  as  long  as  building  was   done   from   the 
freehand   drawings  of  the  artist-mastermason. 
No  painter,  even  of  to-day,  would  draw  in  a 
door  in   one   of  his  pictures  with  a  rule  and 
compasses;  he  knows  that  there  is  a  quality 
in  the  natural  work  of  hand   and   eye  which 
no    artificial    aids    can   give    him.     The    old 
Egyptians  and  the  Greeks  knew  that,  and  the 
tradition  of  it  lasted  on  in  a  few  cases  of  stone 
construction    even    when    the    designs    were 
ruler-made,   and    when    the    irregularities    of 
handiwork   had  become  the  conventions  of  a 
few  skilled   masons.     As  we   have  seen,  two 
English  architects  in  the  seventeenth  century 
recognised    the   existence   of    deliberate   con- 
structional    inequalities.      As     late     as     the 
eighteenth  century  these  principles  prevailed, 
as  may  be   seen  in  the  "humped"  pediment 
of  the  Mansion  House  in  London.     Even  to- 
day the  thatcher  builds   his  cottage  roof  not 
in  straight  lines,  but  in  curves,  which  absorb 
less    rain-water,    and    he    achieves   a  beauty 
which   is   denied  to  the  higher   mathematics. 

four,  and  his  comment  is  : — "In  this  arrangement  there  is 
one  of  the  most  remarkable  instances  I  know  of  the  daring 
sacrifice  of  symmetry  to  convenience,  which  was  noticed 
in  chap.  vii.  ['  Stones  of  Venice/  vol.  ii.]  as  one  of  the 
chief  noblenesses  of  the  Gothic  schools."  But,  of  course, 
questions  of  "convenience"  do  not  enter  into  the  "sym- 
metrophobia  "  discovered  by  Penrose  and  Goodyear. 


vi.]  MODERN   STREETS  113 

The  old  streets  were  full  of  beautiful  curves 
which  cannot  be  explained  only  on  the  theory 
that  twisting  thoroughfares  were  more  easy 
to  defend,  or  by  the  suggestion  that  the  houses 
grew  up  at  haphazard.  Neither  of  these 
reasons  can  explain  the  beauty  of  the  High 
at  Oxford,  or  the  angle  at  which  Magdalen 
Tower  is  set  to  its  own  quad,  or  the 
superiority  of  Regent  Street  and  Piccadilly 
to  Victoria  Street  or  the  Edgeware  Road. 
The  "  whiff  of  grapeshot,"  has  Haussmannised 
modern  Paris  into  a  city  of  straight  lines, 
and  the  next  step  is  the  chessboard  of  the 
American  city,  in  which  every  thoroughfare 
leads  to  nowhere  in  particular.  When  the 
divergencies  in  building  and  in  the  laying  out 
of  streets  were  almost  forgotten,  the  principle 
that  underlay  them  still  survived  in  that  more 
intimate  form  of  architecture  which  is 
furniture  and  domestic  decoration.  In  the 
best  periods  of  Chippendale,  or  Hepplewhite, 
or  Sheraton,  you  find  each  step  in  a  staircase 
gently  bowed  outwards,  or  given  a  waving 
outline  (as  in  fig.  59) ;  you  find,  too,  that  the 
walls  of  the  best  rooms  are  given  slight  curves 
horizontally  as  well  as  vertically;  you  find 
the  subtle  inequalities  of  feeling  handiwork 
in  settee,  and  chair,  and  screen.  But  the 
modern  "  decorator  "  seems  so  fond  of  Euclid, 
that     the    joys    of    the    rectangle    and     the 

H 


114  A   VANISHED   ART  [chap.  vi. 

parallelogram  have  swamped  the  charms  of 
Nature.  He  forgets  that  even  so  common 
an  object  of  his  daily  life  as  the  human  face 
has  two  sides  which  are  quite  different  the 
one  from  the  other. 

Fortunately  for  us,  Leonardo,  that  mighty 
master  of  the  human  face,  lived  when  these 
principles  were  not  so  utterly  forgotten  as 
they  are  now.  He  was  indeed  a  painter 
of  the  Renaissance,  and  the  Renaissance 
influenced  all  his  life  and  art.  But  he 
was  a  man  whose  personality  broke  a  way 
through  the  limitations  of  every  style.  He 
was  a  student  of  Nature  who  had  observed 
that  her  divergencies  were  even  more  im- 
portant than  her  reproductions,  and  who  did 
not  even  shrink  from  saying  that  the  creative 
imagination  of  the  understanding  man  was 
infinite  in  comparison  with  her.  We  shall 
see  therefore  that  when  he  chooses  his 
inspiration  from  such  a  natural  object  as 
one  of  the  shells  to  which  he  devoted 
special  study,  it  is  not  to  imitate  it  slavishly, 
but  it  is  to  reproduce  those  essential  elements 
in  it  which  are  the  causes  of  its  beauty,  and  to 
mould  them  into  new  forms  at  the  bidding  of 
his  own  artistic  genius. 


CHAPTER  VII 

THE    NAUTILUS 

;< .  .  .  Wrecked  is  the  ship  of  Pearl 
And  every  chambered  cell, 
Where  its  dim  dreaming  life  was  wont  to  dwell 
As  the  frail  tenant  shaped  his  growing  shell, 
Before  thee  lies  revealed 
Its  irised  ceiling  rent,  its  sunless  crypt  unsealed." 

MUST   now  return   to   fig.    27, 
and   endeavour   to   examine   the 
reasons  for  that  spiral  line  which 
encircles    the    central    column   of 
the  shell,  for  the  plaits  upon  the 
columella,     as     the     conchologist 
would    say;    for    this    is   a    little 
structural   detail  which   Leonardo 
evidently  noticed,  and  which   has 
not  been  thought  worthy  of  any 
adequate  illustration  by  later  bio- 
logists.     If   it  had   ever  become 
necessary"  (I  can  find  no  other 
word)   to   strengthen    the    central 
supporting    column   or   columella, 
Fig.  29.       without    too    much    enlarging    it 
ceHtheumgiganteum.  OT  adding  to  its  weight,  no  better 
formation  than  this  spiral  could  be  conceived, 

115 


116  THE   NAUTILUS  [chap. 

and  an  almost  exact  parallel  to  it  occurs  in  the 
air-tubes  or  tracheae  of  insects  and  of  plants. 
Though  of  totally  different  origin,  these  air- 
tubes  in  each  case  have  a  spiral  thickening 
of  the  wall,  which  strengthens  them  and  keeps 
them  open,  just  like  a  spiral  coil  of  wire  round 
a  rubber  garden-hose  :  engineers  and  mecha- 
nicians are  of  course  aware  of  this  artful 
method  of  strengthening  a  cylinder  by  means 
of  a  spiral ;  the  cannons  made  by  winding  wire 
round  a  central  core  are  an  obvious  example. 
I  have  not  found  any  good  drawing  of  this 
formation  in  the  tracheae  of  insects,  though 
I  have  seen  an  example  under  a  microscope 
in  the  British  Museum  of  Natural  History. 
The  tube  has  a  delicate  outside  coating,  and 
after  the  death  of  the  insect  the  spiral  (which 
thickens  this  coat)  can  be  pulled  out  and 
examined.  In  just  the  same  way  the  spiral 
band  can  be  unrolled  from  the  air-tube  of  a 
plant,  and  this  is  very  beautifully  illustrated 
in  the  "  Text-book  of  Botany,"  by  Julius 
Sachs  (Second  Edition,  Oxford,  Clarendon 
Press,  1882),  which  gives  on  page  114  the 
longitudinal  section  of  a  fibro-vascular  bundle 
of  Ricinus,  drawn  in  fig.  95,  s,  and  s',  of  that 
book. 

These  spiral  filaments  are  also  found  in 
double  and  triple,  as  well  as  single,  threads. 
The   spiral    vessels   of    the   Chinese  Pitcher- 


vil]  AIR-TUBES  117 

plant  (Nepenthes)  exhibit  a  quadruple  thread, 
as  in  fig.  54,  and  they  have  the  further 
peculiarity  of  being  sinistral,  like  the  rare 
dexiotropic  Voluta.  These  air-tubes  are 
found  in  the  leaf-stalks ;  they  are  closed ; 
and  their  air-contents  only  permeate  their 
enclosing  membrane,  which  is  so  delicate  that 
if  the  thread  on  the  inner  surface  is  uncoiled, 
no  trace  of  the  thin  membrane  will  be  seen 
except  at  the  conical  end  of  the  ruptured 
vessel.  The  air-vessels  of  insects  are  branched 
and  ramified  so  as  to  form  a  set  of  continuous 
tubes,  and  are  framed  to  resist  pressure  from 
without  by  the  elasticity  of  the  fibre  spirally 
coiled  within  them. 

It  is  only  in  the  true  spiral  vessel  that  we 
find  air  in  each  case.  When  plants  have  long 
continuous  tubes,  forming  ducts  for  fluid, 
the  internal  strengthening  is  formed  by  a 
combination  of  broken  spirals  and  rings, 
exactly  as  in  the  windpipe  of  the  Dugong 
we  find  a  spiral  cartilage  terminating  at 
intervals  in  rings. 

In  Dr  Schleiden's  "  Principles  of  Scientific 
Botany,"  translated  by  Dr  Edwin  Lankester 
(London :  Longmans,  1849),  the  nature  and 
origin  of  spiral  fibres  (discovered  by  Malpighi) 
is  very  carefully  explained,  with  diagrams,  on 
pp.  42-47,  and  to  this  I  must  refer  my  readers, 
for  I  have  but  space  here  to  suggest  that  the 


118  THE  NAUTILUS  [chap. 

same  process  observable  in  these  tubes  may 
have  gone  on  in  the  formation  of  the  spiral 
round  the  columella  of  a  shell ;  and  if  so,  it 
might  no  doubt  be  further  shown  that  shells 
with  only  a  single  spiral  need  such  strengthen- 
ing less  than  those  which  possess  eight,  as 
may  be  perhaps  observed  by  a  comparison 
of  fig.  27  with  fig.  33.  Charles  Darwin 
noticed  that  the  clasp  of  a  twining  plant 
round  its  support  was  definitely  strengthened 
by  the  spiral  twist  of  its  own  actual  fibre  (see 
p.  65),  and  the  plaits  on  the  columella  may 
possibly  be  the  result  of  a  similar  set  of 
circumstances.  In  any  case,  this  additional 
growth  has  never  yet  been  satisfactorily 
explained;  it  may  certainly  be  useful,  as  in 
some  way  assisting  the  animal  to  keep  firm 
hold  of  its  shell  by  means  of  a  muscle 
specially  adapted  to  hold  on  by  it.  But 
there  are  many  large  and  thick  shells  in 
which  the  columella  is  perfectly  smooth, 
so  that  in  their  case — whatever  may  be 
true  in  other  instances — the  mode  of  attach- 
ment must  be  different.  The  spiral  line 
which  I  am  now  considering  begins  at  the 
topmost  and  smallest  chamber  of  the  shell, 
and  continues  growing  with  the  external 
growth  to  the  largest  chamber  at  the  bottom. 
It  is  possible,  therefore,  that  this  spiral  may 
have  some  intimate  relation   to  the   body  of 


VII.] 


THE   COLUMELLA 


119 


the  animal  in  whose  dwelling-place  it  occurs, 
But  this  I  am  inclined  to  doubt,  for  the 
reason  that  in  Turritella  lentiginoses  (fig.  52)  it 
does  not  occur  at  all  (though  possibly  because 
the  "  strengthening "  process  was  not  yet 
advisable),  while  if  we  take  Telescopium  teles- 
copium   (fig.    27)   with   its   one   spiral   as   the 


fig.  30. 

Voluta  solandri. 


Fig.  31. 

Voluta  pacijica. 


beginning  of  a  series,  we  shall  find  Ceritheum 
giganteum  (fig.  29)  and  Voluta  solandri  (fig. 
30)  with  two  spirals,  Turbinella  pirum  (fig. 
7)  with  three,  Voluta  vespertilio  (fig.  53)  with 
four,1    Voluta    pacifica     (fig.    31)     with   five, 

1  Cymbium,  the  boat-shell  from  the  African  coast,  has  four 
plaits  upon  its  columella,  but  its  external  formation  is  en- 
tirely different  to  that  of  Voluta  vespertilio  (see  p.  167). 


120 


THE  NAUTILUS 


[chap. 


Turbinella  fusus  (fig.  32)  with  six,  and  Voluta 
musica  (fig.  33)  with  as  many  as  eight,  while 
the  number  is  even  greater  in  Cymbiola 
tuberculata  and  Harpula  fulminata.  What- 
ever may  be  the  real  explanation  of 
these  internal  spirals  which  are  reproduced 
in    every    chamber   of   the    shell,    I   do    not 


Fig.  32. 

Turbinella,  fusus. 


Fig.  33. 

Voluta  musica. 


therefore  think  that  they  can  be  so  intimately 
connected  with  the  anatomy  of  the  living 
organism  as  with  the  structure  of  the 
shelter  which  it  fashions  for  its  home ;  for 
though  it  may  be  true  that  the  number  of 
"notches"   in   the   columella-muscle  of  these 


vil]  ORGANIC  CURVES  121 

shell-fish  corresponds  with  the  number  of 
spirals  round  the  columella  in  each  case, 
the  question  why  these  spirals  exist  remains 
unanswered. 

"  It  is  better  to  take  the  line  and  leave  the 
shell/'  said  Ruskin,  forbidding  his  pupils  to 
admire  or  use  as  ornament  these  "moulds 
or  coats  of  organism,"  however  beautiful  their 
lines.  He  had  evidently  never  looked  inside 
them. 

But  long  before  liuskin's  criticisms  had 
become  an  artistic  shibboleth,  the  inside  of 
shells  had  fortunately  attracted  the  attention 
of  scientific  men  who  possessed  a  combination 
of  talents  as  rare  as  it  is  fruitful.  I  think 
it  was  Professor  Freeman  who  said  once  that 
the  true  historian  should  not  only  know 
everything  about  something,  but  also  some- 
thing about  everything.  That  may  be  a 
counsel  of  perfection ;  but  it  is  an  ideal  that 
is  worth  remembering  in  days  when  too  much 
specialisation  sometimes  darkens  knowledge. 
The  biologist  is  great,  and  the  mathematician 
is  great;  but  greater  still  is  the  man  who 
can  combine  some  of  the  knowledge  that  is 
in  each  without  losing  the  accuracy  of  either. 
Such  a  man,  to  some  extent,  must  have  been 
Sir  John  Leslie,  who  was  the  first  to  indicate 
the  organic  aspect  of  the  curve-line  known 
to    mathematicians    as    the    logarithmic     or 


122  THE  NAUTILUS  [chap. 

equiangular  spiral  (fig.  35).  "This  spiral/' 
he  wrote,  "exactly  resembles  the  general 
form  and  elegant  septa  of  the  Nautilus" 
("Geometrical  Analysis  and  Geometry  of 
Curve  Lines/'  Edinburgh,  1821,  p.  438).  But 
Canon  Moseley  of  Cambridge  went  further. 
He  made  an  exact  geometrical  examination 
of  certain  Turbine  shells  {Phil.  Trans.,  1838, 
p.  351)  which  exhibited  a  spiral  curve  wound 
round  a  central  axis.  This  curve  was  found 
to  be  logarithmic,  and  from  it  could  be 
framed  a  series  of  formulas  by  which  the 
other  conditions  could  be  predicted  as  they 
were  found  to  exist.  The  spires  of  the  shell 
increased  in  breadth  in  an  exact  successive 
series,  each  one  of  which  was  a  multiple,  in 
a  certain  ratio,  of  another.  Thus  the  shell 
must  possess  this  form  and  could  possess  no 
other,  for  its  spiral  logarithmic  curve  re- 
produced itself. 

Canon  Moseley  also  noticed  that  the 
operculum  was  remarkable  for  its  geometrical 
symmetry  in  the  shells  he  examined;  and 
a  process  which  no  naturalist  had  yet  dis- 
covered was  thereupon  ascertained  by  means 
of  a  mathematical  calculation  of  the  revolution 
which  the  operculum  of  the  shell  must  make 
round  its  axis.  By  cutting  any  part  of  the 
shell  in  the  direction  of  the  plane  of  its  axis, 
he   found   that   every   section    gave    a    form 


ID 
CO 


g 
u. 


Zfl 


a 

r3 


»4 


«, 


CO 


^1 

r 


vil]  THE  OPERCULUM  123 

exactly  similar  to  the  form  of  the  operculum  ; 
and  so  he  proved  in  this  way  that  the  form 
of  a  turbinated  shell  is  produced  by  the 
revolution  of  the  perimeter  of  the  figure 
formed  by  the  operculum  round  the  axis  of 
the  shell.  In  the  Nautilus  this  figure  is  an 
ellipse  which  revolves  round  its  minor  axis 
and  increases  in  geometrical  progression  with- 
out ever  changing  its  form  as  it  revolves. 
The  operculum  being  of  a  fixed  form,  as  the 
shell  grew  it  increased  in  size  proportionately, 
and  thus  formed  a  very  convenient  measure 
of  the  shell  itself  and  all  its  parts,  inasmuch 
as  the  curve  of  the  shell  possessed  the  peculiar 
properties  of  the  logarithmic  spiral.  Nor  was 
the  extension  of  this  animal's  dwelling  formed 
by  merely  pushing  the  operculum  forward, 
as  I  suggested  in  speaking  of  the  growth 
of  Scalaria  scalaris  (fig.  22),  but  by  the 
more  precise  method  of  depositing  additional 
matter  along  the  lower  margin  of  the  shell 
which  formed  the  tangent  of  the  curve.  In 
fig.  34  I  have  photographed  a  Nautilus  shell 
cut  in  two  (N.  pompilius  from  New  Britain)  so 
as  to  show  the  spiral  within,  and  this  should 
be  compared  with  fig.  35,  which  was  drawn 
for  me  by  a  Senior  Wrangler  as  an  academic 
example  of  a  logarithmic  or  equiangular  spiral, 
without  any  reference  to  this  paper  or  to  the 
shell  of  which  it  seems  so  close  a  copy. 


1U  THE  NAUTILUS  [chap. 

It  will  be  noticed  here  that  Mr  Church's 
application  of  the  logarithmic  spiral,  as  an 
ideal  formula  for  "  uniform  growth"  to 
phyllotaxis,  will  serve  the  conchologist  equally 
well  in  the  present  instance;  for  certainly 
this  Nautilus  is  so  nearly  a  logarithmic  spiral 
that  the  difference  between  the  two  can 
easily  be  expressed  in  a  mathematical  formula 
which  will  give  —  for  the  first  time  —  an 
accurate  definition  and  description  of  the 
shell.  Professor  Goodsir,  and  Mr  Church 
after  him,  have  considered  that  the  loga- 
rithmic spiral  is  a  manifestation  of  the  law 
which  is  at  work  in  the  increase  of  organic 
bodies  :  "  Spira  Mirabilis,  as  Bernouilli  called 
it  (in  "  Acta  Eruditorum,"  1691),  and  gave 
it  the  motto — " Eadem  Mutata  Resurgo" — 
because  it  reproduces  itself  both  in  its  in- 
volute and  its  evolute.  If  they  are  right, 
the  Ammonite,  of  which  I  reproduce  an 
example  from  the  Lower  Lias  of  Lyme 
Regis  (fig.  36),  has  not  survived  as  a  living 
organism,  because  the  sweep  of  its  curve  is 
not  wide  enough  for  truly  vital  expansion, 
and  does  not,  in  fact,  correspond  so  nearly 
to  their  Curve  of  perfect  Growth  as  the 
living  Nautilus  of  fig.  35.  It  may  be  equally 
significant  that  though  the  more  generous 
outlines  of  Argonauta  Argo  (fig.  37)  do  not 
correspond  to  the  logarithmic  spiral  even  so 


00 
CO 


o 


., 


^ 


CO 


vii.]  SPIRA   MIRABILIS  125 

nearly  as  the  Ammonite,  yet  they  err  on  the 
side  of  increase  instead  of  decrease,  and  may 
therefore  have  had  a  greater  chance  of  survival. 
Similar  comparisons  with  the  logarithmic  spiral 
may  be  profitably  made  in  the  case  of  the 
beautiful  external  spirals  clearly  marked  upon 
the  shells  of  Haliotida  gigantea  from  the 
Corean  Archipelago  ;  of  H.  cunninghamii  from 
Australasia ;  and  of  H.  midae  from  the  Cape 
of  Good  Hope.  The  first  of  these  three  ex- 
hibits an  especially  wide  sweep  in  its  outline 
after  the  first  curves  of  the  spiral  have  begun 
to  grow  and  to  expand.  It  has  been  already 
noticed  (see  note  to  p.  73)  that  curves  closely 
approaching  the  logarithmic  spiral  occur  in 
such  minute  specimens  of  life  as  the  In- 
fusoria, described  by  Stein,  especially  in  Stentor 
Coeruleus ;  so  that  Sir  John  Leslie's  recog- 
nition of  the  "  organic  aspect "  of  this  curve 
was  perhaps  wiser  than  he  realised. 

Biologists  may  not  see  anything  very  pro- 
found in  the  approximation  here  illustrated 
of  a  logarithmic  spiral  to  a  shell;  for  they 
know  that  the  spiral  curves  in  the  Nautilus 
are  due  to  growth  and  gravity  acting  on  an 
elastic  substance,  and  mathematicians  tell  them 
that  the  logarithmic  curve  merely  expresses 
in  a  convenient  form  certain  common  and 
usual  relations.  Still,  there  is  no  doubt 
whatever  that  the   mathematical   curve   pro- 


126  THE  NAUTILUS  [chap. 

vides  an  interesting  definition  of  the  shell,  and 
I  have  never  yet  seen  the  apparently  inevit- 
able corollary  to  this  simple  fact,  which  would 
be  to  explain  what  the  component  factors 
are  which  would  produce  a  logarithmic  curve 
in  the  Nautilus,  and  how  those  factors  would 
have  to  differ  in  order  to  produce  some  other 
curve.  I  would  humbly  suggest  this  as  an 
interesting  thesis  to  future  examiners.  A 
careful  inspection  of  fig.  34  will  also  reveal  the 
astonishing  fact  (which  is  common,  I  believe, 
to  every  Nautilus  and  Ammonite)  that  the  last 
compartment  in  which  the  creature  lived, 
instead  of  being  the  largest  of  all,  is  distinctly 
smaller  than  the  one  behind  it ;  a  very  pretty 
instance  of  Nature's  unexpected  asymmetry, 
which  may  be  perhaps  explained  by  the  results 
of  increasing  age  in  the  inhabitant  of  the  shell. 
This  is  the  only  point  in  which  Dr  Oliver 
Wendell  Holmes  does  not  seem  quite  accurate 
about  his  biology  in  the  beautiful  lines  on  the 
Nautilus,  from  which  I  have  made  several 
quotations. 

In  fig.  38  I  reproduce  a  photograph  of 
the  operculum  of  Turbo  marmoratus.  The 
operculum  of  turbinidce  has  been  called  an 
"eyestone,"  and  a  "sea-bean/'  It  is  a  horny 
or  shelly  plate  secreted  by  gastropods  and 
other  molluscs,  which  serves  to  close  the 
aperture  of  the  shell  when    the    animal    is 


vil]  SPEED   OF  ECLIPSE  127 

retracted.  In  Trochus  the  spiral  on  the 
inner  side  is  as  close  as  a  watch-spring.  In 
Turbo  olearius  it  shows  a  beautiful  figure 
like  a  logarithmic  spiral  with  septa  like  the 
Nautilus. 

I  have  abridged  my  description  of  Canon 
Moseley's  investigations  from  Goodsir's  "  Ana- 
tomical Memoirs/'  edited  by  Sir  .William 
Turner  (Edinburgh,  1868,  vol.  ii.  p.  205  et 
seq.);  and  I  insert  it  here  in  order  to  lay 
stress  upon  the  fact  that  if  any  particular 
class  of  natural  objects  were  to  be  chosen 
by  a  student  for  the  purposes  of  such  a 
mathematical  and  creative  art  as  architecture, 
the  class  of  shells  would  be  the  most  suitable, 
inasmuch  as  they  suggest  with  particular 
appropriateness  those  structural  and  mathe- 
matical problems  which  a  builder  so  often 
has  to  face.  The  deductions  made  by 
Professor  Goodsir  from  Canon  Moseley's 
investigations  will  be  mentioned  later  on  in 
their  proper  place.  It  will  be  appropriate, 
however,  to  point  out  here  that  M.  Vial  de 
Saint-Bel,  a  famous  veterinary  surgeon  and 
anatomist  of  the  eighteenth  century,  made 
very  careful  examinations  and  mathematical 
measurements  of  the  body  and  skeleton  of 
Eclipse,  the  famous  racehorse  which  died  in 
1789.  From  these  a  valuable  series  of 
standards     and     proportions     was     deduced, 


128  THE   NAUTILUS  [chap. 

which  1  have  republished  elsewhere1  as  a 
method  for  comparing  the  developments  of 
the  English  thoroughbred  in  the  past  hundred 
years,  and  as  some  explanation,  from  the 
purely  mathematical  point  of  view,  of  a 
speed  which  was  entirely  owing  to  Eclipse's 
wonderful  anatomical  construction.  The  most 
interesting  result  of  M.  de  Saint-Bel's  in- 
vestigations has  only  recently  appeared ;  for 
he  proved  by  mathematics  that  Eclipse  must 
have  made  certain  movements  with  his  legs 
which  nobody  could  see.  Only  when  in- 
stantaneous photography  was  invented  and 
applied  to  horse-racing,  did  these  movements 
actually  make  their  appearance  in  the 
photograph  of  a  galloping  horse. 

Having  given  an  example  of  "biological 
mathematics"  before  Moseley,  I  will  add  an 
example  of  mathematical  biology  after  his 
time,  from  the  "First  Study  of  Natural 
Selection  in  Clausilia  laminata  (Montagu)," 
which  was  published  in  October  1901,  by 
Professor  W.  F.  R.  Weldon  in  BiometriJca. 
He  pointed  out  that  the  problems  presented 
by  certain  terrestrial  mollusca  in  Europe  are 
of  great  interest  in  connection  with  the  theory 
of  natural  selection,  and  that  such  specific 
(though   apparently   "useless")    characters   as 

1 "  A  History  of  the  English  Turf  (Illustrated).     Messrs 
H.  Virtue  &  Co, 


vil]  CLAUSILIA  LAMINATA  129 

the  shape  of  the  spire,  the  number  of  ridges 
and  furrows  on  a  given  whorl,  or  the  size  and 
shape  of  the  aperture,  can  often  be  expressed 
in  such  a  way  as  "  to  admit  of  numerical  com- 
parison between  individuals/'  The  shell  of  an 
adult  Clausilia  laminata  is  essentially  a  tube 
coiled  round  an  axis  so  that  the  successive 
coils  are  in  contact,  much  as  in  Turritella 
lentiginosa ;  and  by  carefully  determining  the 
pitch  and  measurements  of  both  the  peripheral 
spiral  and  the  columellar  spiral  in  a  number 
of  examples  from  the  beechwoods  of 
Gremsmuhlen  in  Eastern  Holstein,  Professor 
Weldon  drew  various  conclusions.  The 
upper  whorls  of  the  adult  shell,  he  found, 
represent  the  condition  of  the  young  shell, 
from  which  this  adult  was  formed  by  the 
addition  of  new  material,  in  a  practically  un- 
altered form.  Specimens  taken  from  a 
district  which  the  species  is  known  to  have 
inhabited  since  pre-glacial  ages  are  in  such 
equilibrium  with  their  surroundings  that  the 
mean  character  of  the  shell-spiral  is  the  same 
from  generation  to  generation,  and  is  not 
being  changed  by  selection  during  the  growth 
of  a  young  generation.  The  life  or  death  of 
an  individual  is  in  fact  determined  in  each  case 
by  the  value  of  a  number  of  correlated 
characters,  among  which  differences  of 
structure  so  slight  as  that  of  the  measurements 

i 


ISO  THE    NAUTILUS  [chap. 

of  the  spirals  are  associated  with  the  difference 
between  the  survival  and  the  total  extinction 
of  a  race  in  a  particular  locality. 

The  discovery  of  Neptune  by  Adams  and 
Le  Verrier,  owing  to  the  calculations  in- 
volved by  the  observed  aberrations  of  Uranus, 
is  an  instance  of  "  scientific  thought " 
well-known  to  astronomers.  But  another 
example  is  quoted  by  Professor  W.  K. 
Clifford,  which  is  even  more  typical  of  the 
mental  process  to  which  I  desire  to  draw 
attention.  A  dot  on  paper  seen  through 
Iceland  spar  shows  as  not  one  but  two 
dots.  Sir  William  Rowan  Hamilton,  late 
Astronomer  Royal  of  Ireland,  knowing  both 
this  phenomenon  and  Fresnel's  explanation  of 
it,  predicted  that  by  looking  through  certain 
crystals  in  a  certain  direction  we  should  see  a 
continuous  circle,  and  Mr  Lloyd  did  see  this 
circle.  On  page  154  I  have  given  a  remark- 
able instance  of  similar  foresight  in  Leonardo 
himself. 

From  the  fact  that  some  acids  and  salts, 
when  seen  by  a  ray  of  polarised  light,1  show 
spirals  which  turn  either  to  the  right  or  left, 

1  " Airy's  spirals"  is  the  name  given  to  the  peculiar 
coloured  interference-figures  seen  when  two  sections  of 
quartz,  one  of  a  right-handed,  the  other  of  a  left-handed 
crystal,  both  cut  transversely  to  the  vertical  axis,  are 
placed  one  over  the  other,  and  viewed  in  converging 
polarised  light, 


vil]  PASTEUR  131 

modern  investigators  have  been  inclined  to 
take  the  occurrence  of  this  formation  as  a  test 
between  organic  and  inorganic  matter  in  the 
long  argument  as  to  the  possibility  of  breaking 
down  the  distinction  of  vital  force  which  is 
supposed  to  exist  between  the  thing  that  has 
been  "  naturally  "  created,  and  the  thing  which 
is  "chemically  made."  In  his  laboratory  a 
chemist  can  now  make  a  compound,  such  as 
tartaric  acid,  which  will  be  optically  neutral, 
that  is  to  say,  it  will  exhibit  a  mixture  of 
right-handed  and  of  left-handed  spirals,  where- 
as in  Nature  we  find  these  spirals  are  of  one 
kind,  either  right-handed  or  left-handed  in 
each  case.  In  the  laboratory  the  one  kind 
can  be  separated  from  the  other  by  biological 
means,  for  there  is  an  organism  which  feeds 
upon  one  sort  and  rejects  the  other.  Pasteur, 
however,  devised  a  process  by  which  no  such 
biological  assistance  was  necessary;  for  by 
crystallising  the  compound  he  was  able  to 
pick  out  those  salt-crystals  with  their  hemi- 
hedral  face  to  the  right  from  others  which 
exhibited  the  left-handed  formation.  In 
this  way  he  approached  very  near  the 
boundary  which  still  guards  the  mysteries  of 
organic  life ;  and  it  was  the  spiral  formation 
which  enabled  him  to  do  so. 


CHAPTER  VIII 

OF    MASONRY 

"The  stairs  as  he  treads  on  them  kiss  his  feet." 

TN  previous  pages  I  have  attempted  to  give 
some  explanation  of  the  beautiful  spiral 
lines  upon  the  columella  of  such  a  shell  as 
that  shown  in  fig.  53,  which  is  the  fourth  in 
a  series  of  which  Telescopium  telescopium  with 
its  single  spiral  (fig.  27)  is  the  beginning.  In 
fig.  28  I  reproduce  the  photograph  of  an  old 
staircase  in  the  Chateau  of  Blois,  built  long 
before  Leonardo  da  Vinci  came  to  France. 
The  origin  of  the  architectural  lines  in  such 
a  staircase  as  this  is  more  easily  explained 
than  the  structure  either  of  a  Telescopium  or 
of  a  Voluta. 

When  the  first  great  square  or  circular 
feudal  fortresses  or  keeps  were  built,  the  walls 
were  of  such  enormous  thickness  that  the 
space  for  the  living  rooms  was  very  consider- 
ably curtailed,  and  a  staircase  after  the  usual 
London  pattern   would  have  left  hardly  any 

132 


M 


chap,  viil]      LONDON   STAIRCASES  13S 

room  at  all  either  for  the  owner's  family  or  for 
his  garrison.  Yet  it  was  necessary  to  get  access 
quickly  and  easily — in  some  cases  secretly — 
from  one  floor  to  another;  and  when  a  lady 
was  living  in  the  same  building  with  a  number 
of  soldiers,  she  might  desire,  even  in  those 
rough  times  when  dignity  counted  for  more 
than  decency,  to  have  a  separate  staircase  to 
herself,  leading  perhaps  from  her  boudoir  to  the 
dais  of  the  hall,  while  a  different  stairway,  at 
the  opposite  angle  of  the  room,  admitted  the 
crowd  of  men-at-arms  who  sat  below  the  salt. 
To  manage  these  separate  approaches  by  means 
of  two  "  London  staircases  "  would  have  meant 
a  waste  of  room  even  more  fatal  than  our  own 
modern  cramped  arrangements.  The  problem 
was  first  solved,  I  imagine,  by  providing  a 
shaft  in  the  thickness  of  the  wall  from  one 
floor  to  another,  the  entrances  of  which  opened 
in  the  corner  of  each  room.  But  it  would  be 
impossible  to  drop  a  man  down  this  shaft  like 
a  parcel,  still  less  to  climb  up  without  help ; 
and  a  ladder,  whether  of  wood  or  rope,  would 
necessarily  be  at  a  dangerously  acute  angle. 
So  they  began  by  inserting  a  brick  at  the  bot- 
tom of  a  shaft,  just  where  my  piece  of  string 
was  attached  to  the  base  of  the  cylinder  in 
my  first  illustration  (see  fig.  3)  of  an  upward 
dextral  helix ;  only  you  must  now  imagine 
that  the  cylinder  has  become  a  long  hole  in  a 


134  OF  MASONRY  [chap. 

solid  body,  and  that  into  this  containing  circu- 
lar body  a  slab  of  stone  large  enough  to  tread 
upon  has  been  placed  a  foot  above  the  floor. 
Continuing  your  natural  spiral  movement  to 
the  right,  you  must  then  place  another  stone 
in  position,  a  foot  higher  than  the  other,  and 
further  forward — that  is  to  say,  further  round 
this  internal  shaft  up  which  you  wish  to  ascend. 
Continuing  in  this  way,  you  will  gradually  fix 
your  slabs  of  stone  to  the  inside  of  the  shaft  in 
constantly  ascending  spiral  curves  until  you 
reach  the  top ;  and  with  a  little  practice  you 
will  be  able  so  to  adjust  the  angle  of  the  spiral 
that  the  end  of  it  exactly  reaches  the  upper  door- 
way. The  wall  will  always  be  on  your  right 
as  some  support,  but  there  is  a  dismal  cavity 
on  the  left  hand,  and  a  false  step  would  hurl 
you  headlong  through  the  middle  of  the  brick- 
bristling  shaft  to  the  bottom.  To  avoid  this, 
in  your  next  experiment  you  take  rather  longer 
slabs  of  stone  and  diminish  the  danger ;  but  a 
time  arrives  when  you  cannot  increase  their 
length,  owing  to  the  fact  that,  though  one  end 
is  firmly  inserted  in  the  wall,  the  other  stretches 
out  into  emptiness,  and  a  heavy  weight  might 
entirely  displace  it.  This  would  have  been  a 
critical  moment  for  the  builder  whose  shaft  was 
of  a  large  diameter. 

When  Charles  V.  of  France  built  the  grand 
staircase  of  the  Louvre  (since  destroyed),  Ray- 


viii.]  THE   STEPS  TO   HELL  135 

mond  du  Temple  found  that  the  Paris  quarries 
of  1365  could  not  furnish  big  enough  slabs  in 
time,  for  over  six  feet  in  length  was  what  he 
needed.  So  a  selection  of  tombstones  from 
the  Churchyard  of  the  Innocents  was  made ; 
and  I  can  conceive  no  stranger  material  than 
this  "derangement  of  epitaphs."  Surely  the 
Devil  upon  Notre  Dame  must  have  chuckled  ; 
for  of  what  else  are  made  the  steps  which  lead 
to  Hell,  even  if  the  paving-stones  are — on  good 
authority— of  a  different  substance  ? 

But  as  the  first  of  these  primitive  connecting 
shafts  was  probably  quite  small,  I  think  the 
true  solution  of  the  whole  problem  rapidly 
made  its  appearance.  In  the  case  of  a  shaft, 
for  instance,  of  six  feet  in  diameter,  if  all  the 
slabs  of  stepping  stones  projected  3  ft.  6  in. 
from  the  wall  they  would  overlap.  The  first 
case  of  overlapping  may  have  been  an  accident ; 
but,  at  any  rate,  it  was  soon  found  that  this 
method  entirely  covered  up  that  dangerous 
hole  in  the  middle  which  I  mentioned ;  and 
as  soon  as  this  was  effected  the  greatest  dis- 
covery of  all  came  simultaneously  to  light. 
For  as  the  stairway  rose,  a  central  column  was 
seen  to  be  rising  with  it  on  the  left  hand  of 
any  person  ascending  the  dextral  helix  of  the 
stairs  ;  and  by  degrees  the  masons  learned  so 
to  cut  their  stepping-stones  that  this  central 
column  was  not  only  built  up  by  these  stones, 


136  OF  MASONRY  [chap. 

but  also  in  its  turn  supported  them,  for  they 
now  overlapped  both  at  their  ends  and  at  their 
edges.  And  now  at  last  the  outer  wall  on  the 
right-hand  side  fell  into  its  true  position  of  a 
mere  protective  shell,  while  the  essential  feature 
of  the  whole  was  the  central  column  round 
which  the  fan-like  steps  revolved.1 

To  explain  this  first  development  of  the  real 
spiral  staircase  (instances  of  w^hich  may  be 
found  in  most  lighthouses  and  in  the  Tower 
of  London),  I  reproduce  here  a  drawing  by 
Viollet-le-Duc,  which  shows  one  entire  revolu- 
tion of  the  steps,  and  also  gives  the  drawing 
(fig.  39)  of  a  single  step  which  contains  its 
own  portion  of  the  central  pillar,  as  will  be 
found  to  be  the  case  in  the  example  I  repro- 
duced (in  fig.  21)  of  the  Palazzo  Contarini. 
It  will  be  noticed  that  the  architect  has  not 

1  This  explanation  of  the  way  a  spiral  staircase-  was 
evolved  has  high  authority,  and  is  accepted  as  possible 
in  such  valuable  text-books  as  the  "  Century  Dictionary,' ' 
s.v.  "Newel,  .  .  .  "in  stairs  where  the  steps  are  merely 
pinned  into  the  wall  by  their  outer  ends,  and  there  is 
no  central  pillar,  the  staircase  is  said  to  have  an  open 
newel."  But  it  is  only  right  to  state  here  that  some  modern 
architects  refuse  to  believe  that  any  workman  would  pin 
a  step  into  the  outer  wall  without  supporting  it  by  a  beam 
from  beneath,  and  this  is  quite  a  probable  deduction  from 
the  character  and  methods  of  modern  masonry.  I  have 
been  dealing,  however,  with  the  masons  of  a  far  older  and 
more  independent  period,  and  I  incline  to  the  belief  that 
the  explanation  given  above  is  correct. 


VIII.] 


THE   HANDRAIL 


137 


yet  reached   the  idea   of   a   handrail,    and   is 

merely  producing   the   simplest   necessity  for 

internal  communication  without  any  idea  of 

decorative  effect.      Some  kind  of  handrail  for 

the  left  hand  soon  became 

necessary,    and    the    first 

was  probably  a  rope  which 

was  firmly  attached  to  an 

iron   ring  at   the   top    of 

the  stairway  and  followed 

its   curves   down    to    the 

bottom,    being    kept     atB 

the    right    height   by   an 

occasional   staple   on   the 

way.      By     degrees     the 

stone     of      the     central 

column  got   worn  into  a 

regular     groove    by    the 

constant  pressure  of  this 

rope,  and  it  soon  became 

evident  that  the  handrail 

might  become  not  merely 

an    integral   part    of  the 

stonework  of  the  staircase 

but  a  very  definite  addition  to  the  beauty  of  its 

decoration.     Such  spiral  staircases  were  known 

to  the  Romans,  who  left  the  rough  screws  they 

filed  out  among  the  ashes  of  Pompeii,  though 

they  had  not  advanced  sufficiently  in  mechanics 

to  be  able  to  make  a  nut  that  would  actually 


A  B 

Fig.  39. 

Primitive  Spiral  Staircase,  with 
plan  of  one  step. 


138  OF  MASONRY  [chap. 

correspond.  But  the  conditions  of  mediaeval 
life  made  spiral  staircases  peculiarly  valuable  to 
the  feudal  architect,  for  doors  could  open  into 
them  at  any  height  in  their  spiral  upward 
course  ;  they  were  easily  lighted,  and,  at  first, 
of  simple  and  rapid  construction,  which  could 
be  easily  repaired.  They  could  be  held  by  a 
few  men  against  a  hundred  foes  ;  they  joined  the 
very  top  of  the  building  with  the  very  bottom, 
and  the  slope  of  their  ascent  could  be  made 
gentle  or  steep  at  will. 

We  have,  of  course,  long  ago  rejected 
such  useful  and  beautiful  possibilities  in 
London  houses,  which  are  as  narrow  and 
lofty  as  a  feudal  keep,  perhaps  because  we 
could  not  easily  get  our  furniture  and  other 
cumbrous  living-apparatus  up  and  down  a 
spiral;  yet,  with  these  methods,  it  would 
be  possible  to  construct  two  interior  spirals 
where  there  is  now  scarce  room  for  one  narrow 
stairway  and  a  set  of  useless  landings.  The 
danger  of  fire  would  certainly  be  reduced  if 
one  of  these  spirals  were  constructed  of  unin- 
flammable materials,  or  even  built  outside  the 
main  walls  of  the  building.  At  Hertford 
College,  Oxford,  the  architect  seems  to  have 
remembered  a  sixteenth-century  model,  but 
to  have  been  unable  to  find  workmen  capable 
of  carrying  out  a  sixteenth-century  design. 
At  any  rate,  the  result  is  a  somewhat  inelegant 


viil]  TOWER  HOUSES  139 

compromise  between  the  old  and  new.  One 
of  the  largest  "  Newel  -  Staircases  "  in  the 
United  Kingdom  is  at  Fyvie,  in  Scotland. 

It  is  strange  that  the  daily  use  of  this 
beautiful  form  of  staircase  is  almost  entirely 
restricted  (in  the  British  Islands)  to  lighthouse 
keepers ;  for  it  is  only  found  in  towers,  and 
dwellers  in  the  Martello  Towers  along  the 
coast  are  rare.  The  Border  "  Peels "  were 
built  only  for  defence,  as  were  probably  Dacre 
Castle,  in  Cumberland,  or  Belsay,  in  Northum- 
berland. In  Ireland  the  form  survived  much 
later.  In  the  old  part  of  Blarney  Castle,  the 
stone  used  does  not  contain  the  full  circle 
shown  at  "  A,"  in  fig  39,  but  only  a  half  circle, 
with  the  result  that  the  columns  in  the  centre 
of  each  stair  are  only  semi-cylindrical,  and 
exhibit  one  flat  surface.  But  a  very  curious 
fact  I  observed,  there,  is  that  throughout  this 
old  part  of  Blarney,  every  staircase  without 
exception  is  sinistral  in  form,  which  shows  that 
Cormack  McCarthy,  the  Strong,  fully  appre- 
ciated the  advantages  involved  in  having  his 
own  right  hand  free  to  attack  an  ascending  foe 
who  would  only  be  able  to  use  his  left  hand 
in  defence.  There  is  a  spiral  staircase  in  the 
stronghold  of  the  Black  Douglas,  Tantallon 
Castle,  near  North  Berwick,  and  this  also  is 
sinistral,  which  may  be  for  the  same  military 
reason  as  that  suggested  at  Blarney. 


140  OF  MASONRY  [chap. 

As  the  country  became  more  settled,  the 
tower  which  was  first  used  simply  for  safety, 
was  gradually  built  for  pleasure  too,  as  was 
Nunney  Castle,  in  Somersetshire,  or  Friston 
Tower,  near  Ipswich,  or  Middleton  Tower, 
near  Lynn  in  Norfolk,  which  is  of  brick,  and 
still  (I  believe)  inhabited.  But  by  far 
the  most  interesting  structure  of  the  kind,  also 
of  brick,  which  I  have  heard  of  in  this  country 
is  Tattershall  Castle,  in  Lincolnshire,  which 
was  designed  by  no  less  a  person  than  William 
of  Waynflete,  Bishop  of  Winchester, x  for 
Ralph,  Lord  Cromwell,  Lord  Treasurer  of 
England  from  1433  to  1443,  who  built  a 
stately  house  for  himself  in  his  own  country, 
just  as  Chenonceaux  or  Azay  le  Rideau  were 
built  by  Financier  -  Generals  of  France. 
Apparently  his  family  had  no  connection  with 
the  ancestors  of  Thomas,  "  malleus  mona- 
chorum,"  or  of  the  still  more  famous  Oliver, 
both  of  the  same  name.  Many  of  the  fire- 
places in  the  present  House  of  Commons  were 
modelled  after  the  magnificent  specimens  at 
Tattershall,  but  the  feature  of  the  place  which 
I  now  wish  to  emphasize  is  the  grand  staircase  of 
one  hundred  and  seventy-five  steps,  which  is  in 
the  South  East  Turret,  and  gives  communication 

1  See  the  Note  on  Tattershall  Castle  by  Dr  E.  Mansel 
Sympson,  in  "Lincolnshire  Notes  and  Queries/'  for  April 
1900. 





viil]  OPEN   STAIRCASES  141 

to  forty-eight  separate  apartments,  four  of  which 
are  very  large.  Its  stone  handrail,  sunk  into 
the  brickwork,  and  beautifully  moulded  to  afford 
a  firm  hand-grasp,  is  original  in  conception,  and 
probably  unique  in  design.  This  is  the  only 
staircase  in  a  building  eighty- seven  feet  long, 
sixty-nine  feet  wide,  and  one  hundred  and  twelve 
feet  high,  which  is  almost  entirely  constructed 
of  small  and  brilliantly  coloured  bricks  from 
Flanders,  or,  as  some  think,  from  Holland. 
The  curve  of  this  splendid  staircase  is  of  the 
rare  sinistral  formation,  and  is  contained  within 
a  shaft  twenty-two  feet  in  diameter,  built  of 
enormously  thick  walls. 

It  was  soon  found  that  spiral  staircases 
could  not  only  be  built  into  the  interior  of 
a  house,  as  in  the  example  at  Blois  already 
quoted  (fig.  28),  but  that  there  was  a  distinct 
gain  both  in  freedom  of  access  and  in  methods 
of  lighting  when  the  whole  staircase  was  placed 
outside  the  walls,  which  thus  secured  an 
admirable  additional  adornment,  as  is  the 
case  in  the  "  Escalier  a  jour "  of  the  newer 
wing  of  Francis  I.  at  the  same  chateau  (fig. 
58).  By  the  time  this  idea  was  realised,  the 
architect  had  made  a  very  distinct  advance, 
and  the  mason  who  built  for  him  had  attained 
a  skill  which  is  completely  lost  in  his  profession 
nowadays.  The  delicacy  of  measurement 
implied,  for  instance,  in  the  single  stone  and  in 


142 


OF   MASONRY 


[chap. 


the  completed  spiral  of  the  next  stairway  I 
reproduce  from  Viollet-le-Duc  (see  fig.  40), 
can  scarcely  be  appreciated  by  any  one  who 
has    not    endeavoured    to    do    what   is   here 

accomplished.  For  it 
will  be  observed  that 
each  step  is  light  yet 
strong,  and  carries  with 
it  not  only  the  central 
spiral  but  the  handrail 
Ilk.      b  Ji|  as  well,  while  the  con- 

struction  is  so  artfully 
managed  that  the 
solid  central  column 
becomes  lighter  and 
stronger  as  a  hollow 
cylinder,  and,  though 
every  step  is  firmly 
balanced  in  its  place, 
yet  a  stone  dropped 
from  the  top  of  this 
staircase  would  fall  to 
the  bottom  without 
touching  anything. 
The  beautiful  possibilities  of  this  method  of 
construction  were  in  fact  soon  discovered,  and, 
as  is  so  often  the  case  in  other  matters,  men 
went  to  extremes  of  geometrical  enthusiasm 
which  would  be  the  despair  of  modern  work- 
men.    This   may   partly  be  explained  by  the 


B 

Fig.  40. 

Elaborate  Spiral  Staircase,  with  plan 
of  improved  stonework. 


Fig.  41. 


Two  floors  of  the  Chateau  of  Charabord,  showing  the  interlacing  Spirals  of  the 

Double  Staircase.  [To  face  page  143. 


viil]  CHAMBORD  143 

fact  that  life  in  a  feudal  castle  must  have  been 
very  dull  at  best,  and  a  tricky  staircase  like  the 
one  just  mentioned  may  have  been  a  godsend. 
Not  enough  of  them  are  still  in  existence  for 
me  to  give  as  many  examples  as  I  should  like ; 
but  at  Chambord,  in  Touraine,  there  is  still  a 
tour  de  force  in  the  way  of  spiral  staircases 
which  would  be  very  difficult  to  beat  (see  fig. 
41).  It  contains  two  spirals,  one  within  the 
other,  so  arranged  that  a  man  may  ascend  from 
the  bottom,  while  the  lady  is  tripping  down- 
wards from  the  top  ;  yet  they  will  never  meet 
or  see  each  other,  though  their  steps  and  voices 
are  perfectly  audible.  The  thing  is  a  delight 
to  generations  and  armies  of  tourists  at  the 
present  day,  and  the  pleasure  it  gave  the 
courtiers  of  Francis  I.  in  that  Gargantuan 
Abbey  of  Thelema,  in  which  he  combined 
fortress,  hunting-seat,  and  pleasure-palace, 
after  the  dark  days  of  Madrid,  may  better 
be  described  in  the  pleasant  tales  of  a 
Brantome  or  the  picturesque  exaggerations  of 
a  Rabelais.  It  is  not  my  present  purpose  to 
go  more  into  detail  concerning  such  jeux 
d'esprit,  for  I  am  in  search  rather  of  the 
beautiful  in  construction  than  of  the  merely 
bizarre;  but  they  serve  to  show  some  of  the 
possibilities  of  a  spiral,  and  of  the  attractions 
which  it  exerted  upon  a  constructively  imagi- 
native   mind.     In   the   parallel    which   I    am 


144 


OF  MASONRY 


[chap. 


seeking  between  the  lines  of  architectural 
construction  and  the  lines  of  Nature's  work- 
manship, the  central  column  of  a  spiral  stair- 
case is  an  integral  factor,  and  in 
the  older  Blois  staircase  (fig.  28) 
you  will  observe  that  the  decora- 
tion of  this  central  pillar,  and 
the  carving  of  the  single  spiral 
line  that  forms  its  handrail,  have 
already  reached  a  degree  of 
beauty  which  enhances  the  ex- 
quisite masonry  of  the  curved 
flight  of  steps ;  and  the  colon- 
nettes  carved  upon  its  surface 
give  just  the  same  pleasing 
contrast  that  we  noticed  in  the 
"  Prentice's  Pillar  "  (fig.  4).  This 
style  of  decoration  was  in  use 
earlier  still  in  the  fifteenth 
century,  and,  in  the  last  illustra- 
tion I  shall  borrow  from  Viollet- 
le-Duc,  the  wooden  shaft  of 
Fig.  42.  the  now  vanished  College  de 
Central  Wooden  Montaigu  in  Paris  provides  an 
Kth^cK  excellent    example,   not   merely 

de  Montaigu.  of  ^   j^  of  pjjj^  but  of  the 

rare  sinistral  helix  (see  fig.  42).  It  is  worth 
observing,  however,  at  this  stage  of  our  inquiry, 
that  while  it  was  easier  and  more  natural  for  a 
right-handed   architect   to   draw  plans   for    a 


viil]  THE   BEST   STAIRCASE  145 

staircase  with  a  right-handed  spiral,  this 
"  leiotropic  "  formation  is  not  invariably  better ; 
for  a  man  ascending  it  and  turning  perpetually 
to  the  left  (see  fig.  28)  would  always  have  his 
right  hand  free  to  attack  the  defenders,  and 
the  garrison  coming  down  would  expose  their 
left  hands  on  the  outside.  A  left-handed 
spiral  will  fit  into  any  place  where  a  right- 
handed  spiral  will  go  as  a  staircase,  because  a 
door  can  be  pierced  at  any  point  in  its  course, 
and  I  think  it  is  therefore  probable  that  right- 
handed  spirals  are  more  common  in  staircases 
because  architects  are  usually  right-handed, 
and  "build  up"  more  naturally  in  that  forma- 
tion, not  because  such  spirals  are  structurally 
more  convenient. 

Evolved  architecturally  somewhat  after  the 
fashion  I  have  roughly  sketched,  was  the 
staircase  (fig.  28)  already  long  in  use  at  Blois 
in  that  older  wing  of  Louis  XII.,  which 
Leonardo  da  Vinci  saw  when  he  first 
visited  the  chateau.  I  have  now  to  try  and 
imagine  with  what  thoughts  he  saw  it,  and 
what  effects  it  may  have  had  upon  his  busy 
and  speculative  mind  at  the  moment  when  the 
various  problems  were  just  being  considered  of 
that  new  wing  in  the  castle  for  which  Francis 
I.  had  ordered  plans  and  drawings  to  be 
submitted. 


K 


CHAPTER   IX 

THE    EXILE    * 

"  There  are  two  Books  from  which  I  collect  my  Divinity ; 
besides  that  written  one  of  God,  another  of  His 
servant  Nature,  that  universal  and  publick  Manu- 
script, that  lies  expans'd  unto  the  Eyes  of  all :  those 
that  never  saw  Him  in  the  one,  have  discovered  Him 
in  the  other."  —Sir  Thomas  Browne. 

VI7ITH  the  circumstances  of  Leonardo's 
*  *  sojourn  in  France  I  must  not  concern 
myself  too  much,  but  something  must  be  said. 
Within  the  shadow  of  the  lime-trees  on  the 
terraced  garden  of  Amboise  (some  30  kilometres 
down  the  Loire  from  Blois)  there  is  set  a  bust 
of  the  great  Italian,  and  an  epitaph  upon  the 
tombstone  near  at  hand  painfully  records  that 
underneath  it  are  ashes  "amongst  which  are 
supposed  to  be  the  remains  of  Leonardo  da 
Vinci."  It  was  at  Amboise,  at  any  rate,  that 
he  died  on  May  2,  1519 ;  and  the  myth  of 
those  last  moments  in  the  arms  of  his  royal 
patron  at  Fontainebleau  becomes  as  shadowy 
and    unreal    as    the     artistic     reputation     of 

146 





CO 


g 

Li. 


S3    ~ 

2  "8 

"SO 

.a  ^ 

S3  "^ 
O    g 


H3 


chap,  ix.]        ITALIAN   TRAGEDIES  147 

Francis  I.,  a  reputation  which  I  have  always 
thought  to  be  much  exaggerated.  That 
miscellaneous  grave  is  not  calculated  to 
increase  it. 

Leonardo  had  certainly  lived  in  the  Loire 
valley  some  time  before  June  1518,  as  a 
letter  from  him  exists  of  that  date  written 
at  Amboise ;  and  he  may  well  have  reached 
there  in  the  year  before;  for  it  was  in  1516 
that  he  crossed  the  Alps  at  the  request  of 
Francis  L,  in  order  to  live  at  the  manor 
house  of  Cloux.  If  he  had  taken  more 
thought  of  contemporary  happenings,  he 
might  perhaps  have  remembered  that  the 
Loire  valley  was  already  full  of  sinister 
recollections  of  two  great  Italians  whom  he 
had  formerly  served — Ludovico  Sforza,  called 
II  Moro,  and  Caesar  Borgia.  After  taking 
Bayard  prisoner  at  Milan,  only  to  set  him  free 
again,  Ludovico  had  been  betrayed  to  La 
Tremouille  by  his  Swiss  mercenaries,  and  was 
sent  to  the  dungeons  of  Loches,  where  he 
languished  for  nine  years  in  a  sunless  subter- 
ranean cavern  before  he  died.  The  pitiful 
frescoes  and  inscriptions  left  by  II  Moro  in 
his  cell  by  the  banks  of  the  Indre  were 
still  fresh  when  Leonardo  first  saw  the  great 
towers  of  Amboise  across  the  Loire,  which  are 
shown  in  my  frontispiece.  At  Blois,  on  the 
same  stream,  at  Chinon  on  the  Vienne,  the 


148  THE   EXILE  [chap. 

memories  of  Caesar  Borgia  were  scarcely  less 
vivid;  for  it  was  at  Blois  that  Caesar,  who 
was  created  Due  de  Valentinois  as  a  reward 
for  the  Papal  consent  to  Louis  XII. 's  divorce 
which  he  had  brought  to  Chinon,  had  been 
himself  married  to  Charlotte  d'Albret.  The 
French  king  made  his  triumphal  entry  into 
Milan  with  his  new  ally  in  October  1499, 
and  saw  there  for  the  first  time  the  fresco  of 
The  Last  Supper,  and  the  statue  of  Francesco 
Sforza.  By  1501,  their  artist  had  been  com- 
pelled to  leave  Milan,  owing  to  the  catas- 
trophe of  II  Moro,  and  was  military  engineer 
to  Caesar  Borgia.  But  the  career  of  that 
extraordinary  adventurer  was  not  entirely 
suitable  to  prolonged  artistic  patronage,  and 
when  Francis  I.  was  in  his  turn  making  a 
triumphal  entry  into  distracted  Milan,  in 
October  1515,  after  the  Victory  of  Marignano, 
Leonardo  was  again  there  to  hear  another 
French  king's  praises,  and  by  December  of 
that  same  year  he  was  preparing,  with  Fran- 
cesco Melzi,  to  follow  a  new  patron  to  an 
unknown  country  in  the  last  years  of  his 
life. 

His  little  manor,  close  to  the  castle  and 
town,  is  now  called  Clos-Luce,  and  has  hardly 
been  changed  since  it  was  built  by  Etienne 
de  Loup,  steward  of  Louis  XI.  It  has  never 
sheltered  so  many  famous  visitors  as  when  the 


ix.]  LEONARDO'S   DEATH  149 

great  Italian  lived  there,  and  in  it  he  probably 
painted  the  St  John  the  Baptist  of  the  Louvre 
Collection,  besides  making  plans  for  a  canal, 
with  locks,  at  the  confluence  of  the  Sauldre 
and  the  Morantin.1  It  is  probable,  too,  that 
his  hydrographic  map  of  the  Loire  and  its 
affluents,  now  in  the  Codice  Atlantico  of  the 
Ambrosian  Library  at  Milan,  was  made  during 
this  same  sojourn  at  Cloux,  of  which  so  few 
facts  have  been  recorded. 

His  will  was  made  in  April  1519,  though 
the  written  date  is  1518.  He  made  his  pupil 
and  faithful  comrade,  Francesco  Melzi,  his 
sole  executor,  left  him  all  his  priceless  memo- 
randa, of  which  I  have  printed  a  specimen 
page  in  fig.  48,  and  expressed  the  desire  to 
be  buried  in  the  Church  of  the  Royal  Chapter 
of  S.  Florentin  at  Amboise.  There  he  was 
laid  to  rest,  in  the  next  month,  in  the  cloister, 
as  is  known  from  his  burial  certificate.  The 
church  was  destroyed  in  1808,  and  the  skull 
found  on  its  site  by  Mf  Arsene  Houssaye 
cannot,  it  may  be  feared,  be  acknowledged  as  an 
authentic  relic  ;  though  the  two  stones  found 
in  1863  by  M.  Houssaye  at  Cloux,  marked 
"LEO  .  .  .  INC  .  .  /'   seem   a   more  likely 

1  He  also  suggested  connecting  the  Loire  by  an  im- 
mense canal  with  the  Saone  at  Macon,  in  order  to  open 
up  a  new  route  for  commerce  between  the  north  and 
south  of  Europe. 


150  THE   EXILE  [chap. 

indication  of  the  great  artist's  actual  presence. 
King  Francis  I.  was  at  St  Germain-en-Laye 
at  the  date  of  Leonardo's  death,  and  does  not 
seem  to  have  taken  any  notice  of  the  occur- 
rence. Descendants  of  Leonardo's  father l  are 
still  alive,  and  the  successors  of  Maitre  Boreau, 
the  Amboise  Notary  who  drew  up  his  will, 
were  carrying  on  the  business  there  till 
1885. 

The  certificate  of  Leonardo's  burial  shows 
that  he  had  been  engaged  not  as  the  king's 
painter  only,  but  as  "  premier  peintre  et 
ingenieur  et  architecte  du  Boy,  mechanischien 
d'estat."  His  genius  was  of  so  universal  a 
quality  that  I  feel  no  necessity  for  proving 
over  again  that  he  had  turned  his  attention, 
among  many  other  studies,  to  those  of  archi- 
tecture. The  researches  of  J.  P.  Bichter  pro- 
duce more  than  sufficient  evidence  of  this, 
though  no  building  has  come  down  to  us 
which  has  yet  been  recognised  and  agreed  to 
have  been  built  by  him.      "  In   peace-time," 

1  In  Gaye's  "Carteggio  Inedito  d'Artisti"  (quoted  by 
E.  M 'Curdy),  the  date  of  Leonardo's  birth  is  proved  to  have 
been  1452  in  a  list  of  the  household  of  his  grandfather, 
Antonio  da  Vinci,  made  for  taxing  purposes  in  1457, 
which  records  "Leonardo,  son  of  the  above-mentioned 
Ser  Piero,  illegitimate,  son  of  him  and  of  Caterina,  now 
the  wife  of  Accatabriga  di  Piero  del  Vacca  of  Vinci,  5 
years."  Milanesi  accepts  this  evidence  in  his  edition  of 
Vasari. 


ix.]  ARCHITECTURE  151 

he  wrote  to  the  Duke  of  Milan  in  1490,  "  I 
shall  be  of  as  much  service  to  you  as  any  one 
in  whatever  concerns  the  construction  of  build- 
ings "  :  about  the  same  time  the  Vice- General 
of  the  Carmelites  writes  to  Isabella  d'Este, 
concerning  Leonardo,  that  "  his  mathematical 
studies  have  so  drawn  his  tastes  away  from 
painting  that  he  will  scarcely  hold  a  brush," 
and  Sabba  da  Castiglione  says  also  that  "  when 
he  should  have  wholly  consecrated  himself  to 
painting,  in  which  he  would,  no  doubt,  have 
become  another  Apelles,  he  entirely  sur- 
rendered himself  to  the  study  of  geometry, 
architecture,  and  anatomy " ;  and  it  is  signifi- 
cant that  between  1472  and  1499  we  find 
many  important  buildings  in  Lomhardy  by 
unknown  architects,  which  are  so  good  that 
the  tradition  of  collaboration  between  Leon- 
ardo and  Bramante  may  well  be  true.  At 
Pavia  Cathedral,  and  in  the  church  of  Santa 
Maria  delle  Grazie  at  Milan,  this  tradition  was 
so  strong  that  the  corroboration  of  it  lately 
found  in  Leonardo's  manuscripts,  preserved  in 
Milan,  was  only  to  be  expected. 

By  Baron  Henry  de  Geymuller  all  the 
known  architectural  studies  and  writings  of 
Leonardo  have  been  collected,  and  among 
them  may  be  pointed  out  his  design  for 
draining  "  Romolontino "  (the  Romorantin  of 
Francis  I.)  and  his  sketches  for  a  new  royal 


152  THE   EXILE  [chap. 

residence  at  Amboise,  "  with  a  moat  40  braccia 
wide,  and  to  the  right  of  the  castle  a  large 
basin  for  jousting  in  boats." 

Already  the  best  minds  of  his  day  had  tried 
to  grasp  the  problems  of  a  proportion  in  archi- 
tecture which  should  reflect  the  laws  of  con- 
struction and  growth  exemplified  throughout 
organic  life  in  Nature.  Leonardo  took  up  that 
inquiry  in  his  usual  original  and  thorough 
manner,  and  the  investigations  embodied  in 
my  former  chapters  were  all  suggested  by 
materials  in  his  manuscripts.  He  has  left 
sketches  of  columns  with  archivolts  shaped 
liked  twisted  cords,  copied  from  interlacing 
branches.  He  has  left  drawings  of  flowers, 
such  as  Eglantine,  or  Cyclamen,  of  a  delicate 
tenderness  (see  fig.  48),  that  is  only  surpassed 
by  the  loving  accuracy  with  which  he  analyses 
and  depicts  the  growth  and  structure  of  trees 
or  of  mountains ;  accumulating  this  infinity  of 
observation  not  for  its  own  sake  merely,  but 
in  order  to  combine,  and  to  create  afresh ; 
to  invent  with  knowledge,  and  to  design 
without  disorder. 

He  studied  deeply  the  strength  and  resisting- 
power  of  various  materials,  and  was  the  first  to 
produce  an  exhaustive  theory  of  the  fissures  in 
walls.  In  fig.  44  I  reproduce  a  careful  study  of 
the  spiral  forms  of  smoke  and  dust  caused  by  the 
ruin  of  a  building.     He  wrote  much  upon  the 


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IX.]  ANATOMY  153 

nature  of  the  arch,  and  the  results  of  pressure 
upon  it.  There  was  no  problem  of  construc- 
tion that  came  within  his  ken  which  he  did 
not  grapple  and  attempt  to  solve.  The  traffic 
in  a  crowded  city  was  a  difficulty  in  Italy  long 
before  London  had  become  overgrown.  He 
proposed  to  solve  it  with  a  system  of  high  and 
low-level  streets,  such  as  may  be  seen  to-day 
at  Chester,  and  as  has  been  suggested  in  these 
last  months  for  the  new  streets  near  the 
Strand. 

His  notes  and  drawings  of  anatomy  were 
highly  praised  by  so  great  an  authority  as 
William  Hunter,  and  the  downward  stroke  of 
a  bird's  wing,  which  is  supposed  to  be  so  new 
a  revelation  of  the  instantaneous  camera,  was 
noted  independently  by  Leonardo,  as  it  had 
been  drawrn  by  the  quick-sighted  Japanese  of 
his  own  time.  He  observed,  too,  that  as  the 
tips  of  a  bird's  wings  in  flight  go  up  and 
down  as  well  as  onwards,  they  make  a  spiral 
in  the  air  (fig.  45)  which  is  adapted  to  the 
strength  of  wind-resistance  it  has  to  encounter ; 
and  he  made  use  of  this  observation  in  his 
theory  of  flying  machines.  But  in  this  figure 
it  should  be  observed  that  if  the  straight 
line  between  a  and  p  is  the  direction  of 
the  body  of  the  bird  in  flight,  its  wing-tips 
would  be  approximately  on  a  cylinder  whose 
axis  was  ap  and  radius  the  length  of  a  wing ; 


154  THE    EXILE  [chap. 

so  that  a  more  correct  description  would   be 
that  the  movement  of  each  wing-tip  in  flight 
describes  a  line  of  which   each   portion   is  a 
portion  of  a  spiral,  though  the  whole  line  so 
described  is  not  a  spiral.     But  his  keen  obser- 
vation of  a  bird's  wings  has  received  a  much 
more   striking   confirmation.      His   brain   was 
able  to  infer  what  no  human  eye  could  really 
see,  and  when  he  noted  that  the  spiral  formation 
of  a  screw  was   suggested  by  the  movement 
of  a  flying  bird,  it  was  not  till  four  hundred 
years  afterwards  that  the  truth  of  the  infer- 
ence could  be  visibly  demonstrated.1     But  in 
Pearsons  Magazine  for  May  1902,  on  page  506, 
appeared  one  of  Professor  Marey's  photographs 
of  a  flying  pigeon.     I  have   reproduced  it  in 
fig.    46,    and    the    astonishing    accuracy    of 
Leonardo's    eyesight     and     observation    may 
easily  be  verified   by   a   consideration   of  the 
results  produced  by  an  instantaneous  camera. 
The   prophecy   he    made   so    confidently  still 
awaits  its  fulfilment,  but  he  did  much  to  render 
that  fulfilment  possible.      "Pigliera   il  primo 
volo,"  he  cried,  "  il  grande   ucello   sopra   del 
dosso  del  suo  magnoCecero,empiendo  l'universo 
del   stupore,  empiendo   di  sua  fama  tutte  le 
scritture,  e  gloria  eterna  al  nido  dove  nacque." 
His   Essay   on   Flight  is   throughout   of  the 

1  Compare  M.  Vial  de  Saint-Bel's  argument  concerning  a 
galloping  horse  and  its  confirmation,  on  page  128. 


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Fig.  47. 


A  Page  of  Leonardo's  Handwriting.     (From  Leonardo's  ''Manuscript  Note-book 
on  the  Flight  of  Birds. ' ) 


II  predetto  uccello  sidebbe  coll'  aiuto  del  vento  leva- 
-re  ingrande  alteza,  e  cquesta  sia  la  sua  sicurta ;  perch6 
anchora  che  l'intervenissi  tutte  l'anti  dette  revoluzioni, 
esso  a  tenpo  a  ritornare  nel  sito  dell'  equalita  pur- 
-ch&  le  sua  membra  sieno  di  grande  resistenzia,  acc6 
che  possin  sicura  mente  resistere  al  furore  e  impe- 
-to  del  discenso,  colli  anti  detti  ripari,  e  le  sue 
giuuture  di  forte  mascherecci,  e  li  sua  nervi  di  cor- 
de  di  seta  cruda  fortissima ;  e  non  si  inpacci  alcono 
con  ferramenti,  perchfe  presto  si  schiantano  nelle  lor  tor- 
-ture,  o  si  consumano,  per  la  qual  cosa  non  b  da'npacciar- 
-si  con  loro. 


The  bird  above  mentioned  should,  with  the  help  of  the 
wind,  raise  itself  to  a  great  height,  and  this  will  be  its 
safety ;  because,  although  all  the  revolutions  mentioned 
may  happen,  there  is  time  for  it  to  recover  its  equili- 
brium, provided  its  various  parts  are  capable  of  strong 
resistance  so  that  they  may  safely  withstand  the  fury 
and  impetus  of  the  descent,  being  provided  with  the 
safeguards  mentioned,  with  their  ligaments  of  strong 
tanned  leather,  and  their  tendons  of  very  strong  raw 
silk ;  and  no  one  need  trouble  to  use  iron  joints, 
because  they  split  under  the  strain  of  a  twist,  or  wear 
out,  so  that  there  is  no  need  to  trouble  about  making 
them. 


Transcription  by  Giovanni  Piumati,  and  an  English  Version  of  the 

Translation  by  Charles  Ravaisson  Mollien.     [To  face  page  155. 


ix.]  ON  FLIGHT  155 

highest  interest,  and  I  gladly  acknowledge  the 
debt  which  every  reader  will  owe  to  the  public 
spirit  of  its  owner  and  preserver,  Mr  Theodore 
Sabachnikoff.  The  page  I  reproduce  (fig.  47) 
will  serve  at  once  to  show  the  nature  of 
Leonardo's  notes  and  handwriting,  and  to 
indicate  the  kind  of  material  he  left  behind 
him.1 

In  the  Windsor  Collection  of  his  drawings 
there  are  careful  studies  of  flowers,  of  grass 
and   reeds,  showing  the  various  spiral  forma- 

1  The  Notebook  on  the  "  Flight  of  Birds  "  was  written  by 
Leonardo  da  Vinci  at  Florence  in  March  and  April  1505, 
and  left  by  him  in  1519  to  Francesco  Melzi,  who  died  in  1570. 
From  Melzi's  Villa  of  Vaprio  it  was  stolen  by  Lelio  Gavardi, 
and  finally  given  by  Horace  Melzi  to  Ambrosio  Mazzenta  of 
Milan.  From  him  it  passed  to  Pompeo  Leoni,  friend  to  Philip 
II.  of  Spain,  and  by  his  heir  was  sold  to  Galeazzo  Arconati, 
who  gave  it,  on  21st  January  1637,  to  the  Ambrosian 
Library  in  Milan,  where  its  existence  is  recorded  by 
Balthasar  Oltrocchi,  between  1748  and  1797,  and  by 
Bonsignori  in  1791.  All  thirteen  MSS.  of  Leonardo  were 
sent  to  Paris  by  Napoleon  in  1796,  the  Codex  Atlanticus  to 
the  Bibliothfeque  Nationale,  the  twelve  others  to  the  Institut 
de  France.  In  1815  the  Codex  Atlanticus  went  back  to 
Milan,  the  rest  remaining  (by  error)  at  the  Institut, 
where  the  existence  of  this  Treatise  on  Flight  is  noted  by 
the  Sub-Librarian  in  1836.  From  there  it  was  stolen  by 
Jacques  Libri,  as  Lalannes  and  Bordier  noted  in  1848,  and 
was  seen  in  Florence  by  Count  J.  Manzoni  de  Lugo  in  1867, 
who  bought  it  at  Libri's  death  in  1868,  and  died  himself  in 
1889.  In  1892  it  was  bought  by  Theodore  Sabachnikoff, 
and  published  in  Paris  in  1893. 


> 


156  THE   EXILE  [chap. 

tions  of  their  growth  (see  fig.  48).  Water, 
and  the  forms  of  water,  and  of  mountains, 
seem  to  have  attracted  him  very  strongly, 
as  is  suggested  in  the  blue  hills  and  streams 
which  are  the  background  to  "La  Gioconda." 
The  Windsor  Collection  is  full  of  extraordinary 
studies  of  waves  for  his  representation  of  the 
Deluge.  The  great  struggle  of  one  element 
against  another  did  not  appeal  to  him  merely 
as  a  Biblical  dream.  He  examined  currents, 
whirlpools,  and  ripples,  until  he  had  a  host  of 
actual  facts  with  which  to  work;  of  true 
observations  from  which  to  create  his  vision ; 
of  laws  and  principles  by  which  to  guide  his 
imagination.  In  fig.  49  a  and  b  I  have  re- 
produced two  examples  of  the  careful  way  in 
which  he  studied  the  spiral  formations  of  water. 
It  was  for  the  gardens  at  the  chateau  of  Blois 
that  he  made  sketches  of  further  improvements 
for  the  conduit,  with  its  syphon  discharging 
into  the  Loire,  which  was  built  in  1505  by 
Fra  Giocondo,  the  Veronese  architect.  Among 
his  drawings  are  studies  of  the  curves  of  waves,1 

1  "The  waves  of  light  and  sound,"  said  the  Italian,  "are 
governed  by  the  same  mechanical  law  as  that  governing 
waves  of  water."  Though  the  study  of  waves  of  light,  or 
sound,  or  nervous  transmission,  have  yielded  much  more  than 
Leonardo  dreamt  to  modern  research,  I  know  of  no  one  who 
has  specialised  so  fruitfully  upon  the  study  of  waves  as  Mr 
Vaughan  Cornish,  whose  work  on  "  Kumatology ''  stands 
practically  alone.      He  is  now  investigating  all  waves  that 


Fig.  48. 

Study  of  the  Growth  of  Flowers.     By  Leonardo  da  Vinci.     (From  the  Windsor 

Collection.)  [To  face  page  156. 


B 
Fig.  49. 

Study  of  the  Spirals  formed  in  Water.     By  Leonardo  da  Vinci.     (From  the  Windsor 

Collection.)  [To  face  page  157 . 


ix.]  WAVES  157 

and  of  the  effects  of  currents  upon  the  banks  of 
the  mainland  and  of  islands.  In  these  studies 
he  foresaw  the  scientific  advance  which  he  had 
no  instruments  delicate  enough  to  prove,  for 
he  wrote  that : — "  Le  onde  sonore  e  luminose 
sono  governate  delle  stesse  leggi  che  governano 
le  onde  delle  acque"  The  water  system 
of  the  Cher  and  Loire  he  had  thoroughly 
worked  out,  and  recorded  in  a  map  which 
shows  the  relative  position  of  Tours,  Amboise, 
Blois,  Montrichard,  and  other  places  in  Tour- 
aine.  In  this  connection,  too,  he  frequently 
expresses  his  admiration  of  Archimedes,  and 
of  that  great  inventor's  famous  screw  which 
raised  up  water  by  the  revolution  of  a  pipe 
twisted  in  a  dextral  helix  round  a  rod. 

I  have  already  mentioned  his  particular 
interest  in  shells,  and  in  the  study  for  the 
head  of  his  "Leda,"  which  I  reproduce  in 
fig.  43  at  the  head  of  this  chapter,  it  is  im- 
possible to  avoid  the  parallel  between  the 
twisted  coils  of  the  Ammonite  he  knew  (corn- 
occur  at  the  common  surface  of  two  bodies  which  move 
relatively  to  one  another,  and  his  field  is  vast  and  fruitful, 
for  it  contains  such  various  subjects  as  the  sand-dunes  of 
the  Nile  Delta,  the  ripple-marks  on  hills,  the  ice-folds  of 
glaciers,  the  waves  of  snow,  of  lava,  and  of  air  (created,  for 
instance,  by  a  bullet),  besides  the  waves  in  rivers,  lakes,  and 
seas.  The  results  of  Mr  Cornish's  work,  beautiful  as  they 
are  in  themselves,  will  also  have  a  most  valuable  indirect 
bearing  upon  important  and  practical  inventions. 





158  THE*  EXILE  [chap. 

pare  fig.  36)  and  the  spiral  tresses  into 
which  the  woman's  beautiful  abundant  hair 
is  plaited.1 

He  even  investigated  the  structure  of  in- 
testines, and  it  may  be  noticed  that  the  draw- 
ing in  fig.  50  of  the  section  of  a  shark's 
intestine  gives  a  peculiarly  interesting  example 
of  a  dextral  helix,  the  prime  use  of  which  is  to 
ensure  that  the  food  passes  slowly  round  and 
round  the  tube  in  order  that  every  atom  of 
nourishment  may  be  extracted.2  A  very 
beautiful  parallel  to  this  exists  in  the  internal 
formation  of  Auricula  auris-midce  (fig.  52), 
and  still  more  clearly  in  that  of  Turritella 
lentiginosa  (fig.  51),  a  shell  in  which  you  may 
easily  imagine  yourself  going  up  that  "  little 
tower  "  on  a  continuous  inclined  plane  without 
any  steps  at  all. 

It  is  curious,  to  say  the  least  of  it,  that 
when  Leonardo  was  living  at  Amboise  there 
existed  a  staircase  built  in  the  great  tower  by 

1  In  another  manuscript  he  compares  the  spirals  of  a 
woman's  curls  to  the  circling  of  a  whirlpool. 

2  The  spirals  occurring  in  intestines  and  other  internal 
organs  are  numerous,  and  will  occur  to  every  biologist.  A 
simple  instance  occurs  in  the  ccecum  of  the  rabbit  (Lepus 
cuniculus),  one  part  of  which,  leading  to  the  vermiform 
appendix,  is  wide  in  calibre,  diminishing  somewhat  towards 
its  termination,  thin  in  its  walls,  and  spirally  constructed 
externally  in  correspondence  with  the  spiral  valve  developed 
internally. 


IX.] 


INCLINED  PLANES 


159 


Charles  VI I L  on  exactly  this  model,  and  the 
great  round  tower  which  contained  it  is  shown 
in  Leonardo's  drawing  of  Amboise  which  forms 
the  frontispiece  to  this  volume.1  You  might 
drive   a   carriage   and   pair   down   its   sloping 


Fig.  50.  Fig.   51. 

Longitudinal  Section  of  Turritella 

Intestine  of  Raia.  lentiginosa. 


Fig.  52. 

Auricula  auris-midm. 


circular  curves  to-day  without  meeting  a 
single  step  in  all  the  distance;  and  the 
Emperor  Charles  V.  did,  as  a  matter  of  fact, 
ride  up  it  on  horseback  by  torchlight  during 

1  A  visitor  to  Amboise  would  have  to  hold  Leonardo's 
sketch  before  a  mirror  in  order  to  recognise  that  this  tower 
is  drawn  in  its  right  place. 


_ 


160  THE   EXILE  [chap. 

one    of    his    ceremonious   visits    to   his   rival 
Francis  I. 

After   all   this,  shall   I   be   accused  of  too 
much  special  pleading  if  I  suggest  that,  to  one 
who   had   thus   investigated   the   secret  prin- 
ciples of  construction  and  of  growth,  and  who 
was  especially  attracted  by  the   problems   of 
spiral   formation,   this   inclined   plane   of   the 
spiral   staircase   at   Amboise,  and   this   single 
helix  of  the  old   stair   at   Blois,  presented   a 
greater  attraction  than  that  of  merely  archi- 
tectural problems  skilfully  surmounted  ?     And 
is  it  too  much  to  infer  that,  for  one  who  had 
so  carefully  investigated  the  shells  of  Tuscany, 
Lombardy,  and  Piedmont,  the  comparison  of 
the   Amboise    building   to    Turritella,  and  of 
the   Blois   stair  to    Telescopium,  was   no   im- 
possibility?     Those     two     Italian    staircases 
already  mentioned,  built  by  unknown   artists 
in   Fiesole   and  Venice,  are   both   of  such   a 
period    that,   if   Leonardo   had   ever    studied 
a  shell   in   connection  with   the  architectural 
drawings    for    either,   the    names    they   both 
bear  may   well   be    the    popular    recognition 
of  his  skill  in  constructive  adaptation.     It  is 
interesting,   too,  to   find   that   John   Bellini's 
Allegory  of  the   Shell   (p.    51),  was   painted 
for  the  Contarini  family,  and  that  their  Scala 
del  Bovolo  has  always  been  referred  by  tra- 
dition   to    a    French    model,    which    is    not 


ix.]  OLD  AGE  161 

without  a  certain  suggestiveness  as  to  the 
investigations  of  the  great  Italian  exile  in 
that  valley  of  palaces  which  is  Touraine. 

In  considering  the  possibility  of  such  studies 
in  parallelism  of  structure  having  occupied 
the  leisure  of  a  great  designer,  it  will  be  only 
natural  to  look  for  the  evidences  of  any 
practical  result  towards  the  end  of  a  life 
in  which  busy  activity  would  for  the  most 
part  postpone  such  delicate  imaginations  until 
increasing  years  had  brought  more  oppor- 
tunities of  investigation  and  research.  When 
Leonardo  reached  Touraine  he  was  nearing 
the  end  of  a  life  that  had  been  crowded  with 
creative  action.  The  full  fruit  of  one  of  the 
most  strenuous  and  original  careers  ever  known 
was  in  the  autumn  of  its  ripeness.  Many  of 
the  problems  which  that  fertile  brain  attacked 
have  never  yet  been  solved,  and  if  I  finally 
trace  to  its  marvellous  inventiveness  a 
creation  that  no  recorded  architect  has  yet 
been  found  worthy  to  claim,  it  is  chiefly 
because  the  beauty  of  that  creation  of  man's 
handiwork  remains  unparalleled  outside  the 
realm  of  Nature. 

As  I  approach  this  last  portion  of  my 
argument,  I  must  again  refer  to  that  series 
of  internal  spirals  in  shells  which  I  mentioned 
before,  beginning  with  the  single  line  of 
Telescopium    telescopium    (fig.    27),    or    even 

L 


162  THE   EXILE  [chap. 

further  back  with  the  mere  inclined  plane  of 
Turritella  lentiginosa  (fig.  51),  and  ending  in 
the  eight-fold  curves  of  Voluta  musica  (fig.  33). 
In  that  series  I  wish  now  especially  to 
emphasize  Voluta  vespertilio  (fig.  53)  and  the 
four  particularly  graceful  lines  of  its  dextral 
helix.  But  I  must  also  point  out  the  beautiful 
lines  observable  in  its  external  shape  (fig.  56), 
which  are  not  quite  parallel,  yet  satisfy  the 
eye  completely  in  their  gradual  upward  ascent. 
You  will  notice,  too,  that  the  main  external 
walls  of  the  shell  are  buttressed,  as  it  were, 
with  little  outstanding  columns  which  hold 
up  the  first  of  the  ascending  lines  in  a  manner 
that  would  be  at  once  suggestive  to  an 
architectural  eye. 

We  have  already  observed,  both  at  Venice 
and  at  Chartres,  the  strange  correspondence 
between  the  exterior  arrangement  of  a  stair- 
case and  the  external  shape  of  a  shell.  At 
Blois,  in  the  old  stairway,  we  have  seen  an 
internal  single  spiral  closely  corresponding  to 
the  internal  single  helix  of  the  columella  in  a 
shell.  I  have  now  to  point  out  an  archi- 
tectural example  which  combines  both  these 
correspondences,  and  does  this  although  no  one 
who  only  looked  upon  the  exterior  of  the 
"Escalier  a  jour"  at  Blois  (fig.  58)  would 
dream  of  what  it  contained  within,  any  more 
than  a  person  ignorant  of  biology  who  looked 


ix.]  CLOSE   RESEMBLANCES  163 

at  the  outside  of  Voluta  vespertilio  could 
imagine  the  existence  of  the  quadruple  helix 
inside  it.  When  it  was  only  the  outside,  or 
only  the  inside  of  a  staircase  that  suggested 
the  lines  of  a  shell,  the  evidence  may  not 
have  been  sufficient  to  argue  any  connection 
between  the  one  and  the  other  in  the  builder's 
mind.  But  what  if  the  external  plan  be  the 
same  in  both  a  staircase  and  a  shell,  and  if  the 
internal  spiral  of  the  stair  be  an  exact  copy 
of  the  columella  within  the  same  shell,  even 
to  the  number  of  its  revolutions  round  the 
shaft?  And  what  if,  in  addition,  these 
arrangements  are  in  each  case  carefully 
reversed  in  every  detail  ? 


CHAPTER  X 

THE    SHELL    OF    LEONARDO 

"  Majestati  Naturae  Par  Ingenium  " 

A  T  Blois  there  is  a  staircase  built  later  than 
^  the  old  example  shown  in  fig.  28,  built 
just  at  a  time  when  Leonardo's  presence  in 
Touraine  might  have  enabled  him  to  suggest 
its  plan,  built  with  its  external  lines 
corresponding  to  the  outside  of  a  shell, 
while  its  internal  spiral  reproduces  the  helix 
on  the  columella  of  that  shell. 

In  the  known  examples  of  Voluta  vespertilio, 
about  one  in  a  million  contains  a  sinistral 
helix  instead  of  the  ordinary  dextral  curve. 
I  have  mentioned  an  instance  where  such  a 
rare  shell  at  Travancore  was  considered  to 
have  been  a  manifestation  of  the  Deity.  It  is 
therefore  probable  not  only  that  travellers 
would  try  to  select  one  of  this  kind  to  bring 
home,  but  also  that  in  the  case  of  shells 
common  on  the  seaboard  of  Italy,  the  chief 
reason  for  the  presence  of  one  of  them  in  the 

164 


Fig.   55. 

Escalier  a  Jour,  Chateau  de  Blois,  Touraine.     The  Central  Shaft. 

[To  face  page  165. 


CHAP.  X.] 


FORMS  OP  VOLUTA 


165 


cabinet  of  an  Italian  collector  would  be  that 
it  was  distinguished  above  its  million  fellows 
by  the  possession  of  this  rare  sinistral  helix. 

Compare  the  Voluta  in  figs.  53  and  56  with 
that  shown  in  figs.  54  and  57,  and  in  the  two 
latter  instances  you  will  see  that  the  spirals 
are  reversed,  that  the  "  entrance "  is  on  the 
left  instead  of  on  the  right,  and  that  the 
external  lines   slope  down  from  left  to  right 


Fig.  53. 

The  Common  Form  of  Voluta 
verpertilio  (section). 


Fig.  54. 

Eare  Form  of  Voluta 
vespertilio  (section). 


instead  of  from  right  to  left.  Figs.  53 
and  56  show  the  ordinary  leiotropic  shell 
with  a  right-handed  spiral.  Figs.  54  and  57 
show  the  rare  dexiotropic  shell  with  a  sinistral 
or  left-handed  spiral. 

With   this   exceptional    formation   in   your 
mind,    remembering   also    that    the    ordinary 


166        THE  SHELL  OF  LEONARDO     [chap. 

ascending  curve  described  by  a  right-handed 
man  is  to  the  right,  compare  the  magnificent 
spiral  within  the  staircase  of  the  wing  of 
Francis  I.  at  Blois  (fig.  55)  with  the  helix 
in  the  leiotropic  Voluta  vespertilio  (fig.  53). 
It  is  identical  in  form,  even  in  the  fact  that  it 
is  four  times  repeated,  but  it  is  reversed. 


Fig.  56.  Fig.  57. 

Common  Form  of  Voluta  vespertilio.         Rare  Form  of  Voluta  vespertilio. 

Then  compare  the  external  balustrades 
(fig.  58)  with  the  lines  on  the  outside  of  the 
same  shell  (fig.  56).  They  are  arranged  in 
the  same  way;  they  are  similarly  supported 
by  slender  columns;  they  show  the  same 
charming  and  curious  irregularity,  which 
seems  inexplicable  apart  from  their  model; 
but  they  are  reversed.  Notice  also  that  any 
ordinary  architect  would  have  made  the  lines 


Fig.   58. 


Escalier  a  Jour,  Chateau  de  Blois,  Touraine.     The  Exterior. 

{To  face  page  166. 


x.]  AGREEMENTS  AND  DIFFERENCES  167 

of  his  external  balustrades  correspond  with  the 
main  external  lines  of  the  floors  in  the 
building  to  which  this  open  staircase  was 
added,  if  the  designer  of  the  internal  stairway 
had  merely  wished  to  build  a  four-fold  spiral 
round  its  central  column.  But  the  designer 
of  this  staircase  had  not  merely  a  quadruple 
mathematical  line  in  his  mind,  he  was  think- 
ing of  a  shell ;  and  he  was  not  thinking  of 
Cymbium,  a  shell  which  has  four  plaits  on  its 
columella  and  an  exterior  quite  different  to 
that  shown  in  fig.  56,  but  of  Voluta  vespertilio, 
which  hides  its  quadruple  helix  behind  an 
arrangement  of  sloping  lines  growing  above 
slender  columns,  exactly  as  these  sloping 
balustrades  are  built. 

Look  finally  at  the  doorway  opening  to 
the  staircase  from  outside.  It  is  in  the  same 
relative  position  as  the  "entrance"  of  the 
shell ;  but  it  is  reversed. 

There  are  therefore  no  less  than  four 
instances  of  agreement  with  the  common 
shell,  though  in  any  one  of  these  four  a 
trifling  difference  would  not  have  mattered  to 
the  construction.  And  in  all  these  four 
instances  there  is  an  invariable  and  exact 
reversal,  although  again  there  might  have  been 
trifling  variations  in  plan  made  by  any  one 
who  had  not  got  the  shell  before  him. 

Can  such  agreements  and   such  differences 


168        THE   SHELL   OF   LEONARDO     [chap. 

be  chance  alone?  Can  such  lines  be  the 
result  of  a  merely  architectural  solution  of 
the  problem?  Can  they  be  merely  one  more 
example  of  what  we  have  seen  already,  of 
the  fortuitous  correspondence  between  perfect 
workmanship  and  the  lines  of  Nature  ? 
Surely  they  must  be  a  deliberate  copy  of  the 
natural  object  they  so  closely  imitate ;  yet 
not  an  ordinary  copy,  but  a  copy  with  the 
very  striking  and  logical  and  persistent 
differences  we  have  just  noticed. 

This,  in  fact,  must  be  an  example  of  that 
greatest  art  which  imitates  the  greatest  models 
with  a  difference  that  reveals  the  strength 
and  personality  of  the  designer;  which 
discards  the  trivial  and  preserves  the  essen- 
tial ;  which  loves  knowledge  much,  and  is 
therefore  unafraid  of  novelty ;  which  realises 
the  existence  and  the  value  of  a  studied  excep- 
tion here  and  there  among  all  ordered  things ; 
which  can  unite  design  with  fact,  and 
originality  with  truthfulness ;  which  has,  in 
fact,  discovered  that  the  beauty  of  Nature  is 
not  to  be  found  in  agreement,  but  in 
difference. 

Such  a  creation  as  this  might  well  have  been 
one  of  the  few  practical  results  of  that  philo- 
sophy which  was  expressed  in  the  words : 
"Natural  things  are  finite,  but  man's  handi- 
work is  infinite  "  ;  a  saying  which  was  not  likely 


x.]  NATURE  IS  FINITE  169 

to  have  been  uttered  by  one  who  could  have 
permitted  many  such  works  to  survive  him. 
For  this  man  had  realised  that  in  the  per- 
fection of  Nature  there  is  an  end  attained,  un- 
changing, because  perfect  in  its  kind ;  but  that 
we  are  "  something  better  than  the  birds  or 
bees,"  and  in  our  best  building,  as  in  our  best 
art,  the  confession  of  that  superiority  must 
always  be  found.  Hence  comes  that  nobler 
love  of  change  which  is  the  divine  unrest  of 
genius,  which  often  leaves  so  little  done  behind 
it,  because  there  is  always  so  much  still  to  do. 
Some  faint  suggestion  of  this  feeling  is  to  be 
found  in  the  expression  on  the  face  of  "  Mona 
Lisa."  Not  of  any  mortal  handiwork  were  the 
words  written,  "  Behold,  it  was  very  good  "  ;  for 
labouring  humanity  is  driven  forward  through 
the  ages  by  the  constant  search  for  something 
higher  that  is  ever  hidden,  yet  ever  to  be 
revealed. 

If  then,  as  1  believe,  this  staircase  was  copied 
from  a  shell,  the  man  who  owned  the  shell  and 
used  it  so  must  have  been  not  merely  an  archi- 
tect but  a  master  of  construction,  for  the  groin- 
work  and  vaulting  of  the  stairs  (fig.  59)  are 
not  the  least  astounding  part  of  the  whole 
building ;  and  he  must  have  been  a  decorative 
artist,  too,  of  the  very  highest  order.  Con- 
fining your  attention  for  a  moment  to  the 
inside  of  the  staircase  only  (fig.  59),  you  will 


no        THE   SHELL  OF  LEONARDO     [chap. 

see  ample  evidence  of  this  in  several  directions. 
The  stairs  wind  upwards,  folding  round  that 
exquisite  central  shaft  as  the  petals  of  a  flower 
fold  one  within  the  other;  and  in  the  very 
lines  of  each  step  itself  a  strange  and  beautiful 
look  of  life  and  growth  is  produced  by  the 
double  curve  on  which  it  is  so  subtly  planned ; 
for  these  steps  are  not  straight,  as  in  the  older 
staircase  of  the  chateau,  and  in  most  ordinary 
instances,  but  are  carved  into  a  sudden  little 
wave  of  outline  just  where  each  one  springs 
out  from  the  supporting  pillar — from  the  sup- 
porting stalk,  as  it  were,  of  these  delicately 
encircling  leaves.  Though  I  am  more  con- 
cerned with  constructive  lines  than  with  mere 
decorative  detail,  it  is  impossible  also  to  over- 
look the  set  of  these  colonnettes  that  move 
upwards  with  the  rising  shaft,  and  the  splendidly 
sculptural  treatment  of  the  shells  which  are  set 
between  the  twisted  capitals  of  each  (fig.  55). 
I  would  draw  particular  attention  to  these, 
because  if  they  were  placed  here  by  the  man 
who  was  inspired  to  take  his  original  model 
from  a  shell,  they  would  be  treated  very 
differently  from  any  ornaments  subsequently 
affixed  by  a  lesser  artist  with  a  lesser  inspira- 
tion. And  this  is,  as  a  matter  of  fact,  exactly 
what  is  to  be  found  here.  These  shells  are 
broadly  carved,  with  light  and  shadow;  not 
with  a  mere  imitation  of  exact  form,  but  with 


Fig.   59. 

Vaulting  and  steps  of  Spiral  Staircase  in  the  wing  of  Francois  I.,  Chateau  de  Blois. 

[To  face  page  170. 


x]  SUBSEQUENT  ADDITIONS         171 

a  fine  feeling  for  their  effect  in  this  exact  posi- 
tion. Beneath  them  are  weakly  conventional 
embroideries  of  later  date,  that  are  not  merely 
meaningless,  but  are  cut  off  at  the  bottom  by 
the  ascending  spiral  in  a  way  which  no  one  but 
a  sculptor  devoid  of  all  structural  adaptability 
could  have  permitted.  They  must  be  addi- 
tions of  about  the  same  date  as  the  statues  set 
upon  the  exterior  some  fifteen  years  after  the 
original  structure  had  been  built.  They  are 
repeated  in  the  rooms  of  Catherine  de  Medici 
above,  and  may  be  seen,  in  exactly  the  same 
setting,  on  the  shaft  of  the  great  stairway  of 
Chateaudun,  a  structure  so  complicated  with 
archways  and  landings  that  the  fine  right- 
handed  spiral  of  the  central  column  almost 
loses  its  effect. 

Yet  it  is  the  irresistible,  spontaneous,  uplift- 
ing movement  of  the  whole  that  remains,  after 
all,  the  main  impression  of  this  marvellous 
piece  of  work  at  Blois.  To  walk  up  those 
steps  is  to  be  borne  along  upon  a  breath  of 
beauty,  and  not  to  feel  the  clogging  feet  of 
human  clay  at  all.  Those  waving  lines  rush 
upwards  like  a  flame  blown  strongly  from 
beneath;  for  there  is  in  them  a  touch  of 
that  spell  which  is  elemental ;  of  that  same 
Nature's  mystery  which  curves  the  tall  shaft 
of  the  iris  upwards  from  the  pool  in  which 
it  grows,  or  flings  the  wave  in  curving  lines 


m        THE  SHELL  OF  LEONARDO     [chap. 

of  foam  upon  the  rocks  the  rising  tide   will 
cover. 

He  who  made  all  this,  and  who  owned  the 
shell  which  first  suggested  it,  must  have  been 
an  architect  of  powerful  originality  and  an 
artist  of  extraordinary  imagination,  with  a 
sense  of  harmonious  proportion  rarely  equalled 
in  the  world,  a  sense  which  he  had  trained 
in  many  various  arts  and  many  branches  of 
science,  for  he  must  have  been  a  student  of 
biology  who  collected  natural  objects  with  a 
determination  to  penetrate  the  secret  of  their 
beauty,  just  as  one  of  the  greatest  of  our 
modern  sculptors,  Gilbert,  has  studied  the 
bony  forms  of  fishes,  and  from  them  designed 
the  most  exquisitely  curved  armour  and  the 
most  fantastically  beautiful  ornaments.  Learn- 
ing and  taste  so  universal  as  this  seems  to 
indicate  have  been  rare  at  any  period  of  the 
world's  history :  between  1500  and  1519  there 
was  certainly  but  one  man  who  possessed  them, 
and  that  was  Leonardo,  the  artist,  architect, 
and  biologist,  who  devoted  so  much  of  his  life 
to  the  study  of  the  intercommunication  Be- 
tween art  and  nature ;  who,  in  fact,  did  even 
more  in  this  direction  in  the  fifteenth  century 
than  Gilbert  or  any  other  artist  did  in  the 
nineteenth ;  who  gave  this  final  manifestation 
of  his  constructive  genius  to  France's  ungrate- 
ful monarch  just  before  he  died ;   who  came 


x.]  VOLUTA   NOT  FRENCH  173 

from  those  Mediterranean  shores  where  Voluta 
vespertilio  (which  is  not  a  French  shell)  was 
known. 

Professor  W.  R.  Dunstan,  F.R.S.,  has  been 
kind  enough  to  give  me  a  Voluta  from  the 
Barton  Beds  of  the  Eocene  Age  on  the  coast 
of  Hampshire,  where  there  are  a  very  large 
number  of  these  shells  to  be  found  in  so  re- 
markable a  state  of  preservation  that  they  seem 
scarcely  fossilised  at  all.  In  the  days  of  Leo- 
nardo, and  of  course  long  before  him,  Voluta 
had  vanished,  as  a  living  form,  from  the  Eng- 
lish and  French  coasts  and  from  all  waters  that 
were  colder  than  Italian  seas.  I  have  not  re- 
produced the  English  specimen,  as  it  does 
not  advance  my  argument,  though  its  lines  are 
even  more  beautiful  than  those  of  the  Medi- 
terranean shell  known  to  Leonardo  da  Vinci. 

His  death  occurred  in  May  1519,  only  some 
twenty  miles  from  Blois,  at  that  Amboise 
where  he  had  been  living  for  some  time.  The 
first  payments  recorded  for  the  new  wing  at 
Blois  containing  this  staircase  were  made  by 
Baron  de  Joursanvault  in  July  1516,  just  six 
months  after  the  French  King  had  arranged 
for  Leonardo's  departure  from  Milan.  The 
most  cursory  inspection  of  the  plan  of  the 
whole  building  will  show  that  such  an  external 
feature  may  well  have  been  completed  after 
the  main  lines  of  the  building  had  been  laid. 


174        THE    SHELL    OF   LEONARDO     [chap. 

Its  beauty  is  artfully  thrown  into  relief  by 
the  comparative  simplicity  of  the  wall  from 
which  it  springs.  So  perfect  a  whole  as  is  the 
staircase  may  well  have  taken  many  years  to 
finish,  after  Leonardo  had  given  the  first 
masterly  sketches  of  its  plan.  Some  stones 
in  it  have  been  left  untouched  until  this  day, 
and  a  few  are  only  roughly  chiselled  out. 
Above  and  around  the  entrance  are  three 
statues  which  are  very  characteristic  of  a 
master  of  a  much  later  period,  Jean  Goujon, 
who  was  carving  at  Ecouen  in  1544.  His 
help  may  well  have  been  called  in  to  put  the 
finishing  touches  to  a  structure  which  a  greater 
than  he  had  originated.  No  subsequent  adorn- 
ments could  alter  or  weaken  the  beauty  of  the 
main  conception. 

The  sinistral  curve  within  it  is  rare  in  any 
architecture,  and,  as  I  have  pointed  out,  it  is 
an  exact  reversal  of  the  spiral  contained  within 
the  ordinary  Voluta.  It  would  have  suited 
the  internal  and  external  arrangements  of  the 
rest  of  the  building  just  as  well  if  the  drawings 
for  this  staircase  had  been  made  on  the  plan 
of  the  ordinary  dextral  helix  which  is  exhibited 
in  its  simplest  form  in  the  staircase  built  at 
Blois  (fig.  18)  before  Leonardo  came  to 
France.  There  is  no  constructive  reason, 
therefore,  for  the  reversal,  and  a  probable 
reason  for  any  designer  putting  a  left-handed 


PQ 


o 


ff 

V 


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vl      ft     fr~T  *T- 


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Star     \*\ 


id? 


x.]  LEFT-HANDED  175 

spiral  into  his  sketches  would  be  that  he  was 
himself  left-handed. 

Leonardo  da  Vinci  was  left-handed.  Ninety 
per  cent,  of  the  screws  and  spirals  contained  in 
his  manuscripts  are  left-handed  spirals,  and  in 
fig.  60  I  have  reproduced  five  of  these  out  of 
a  great  number  similarly  drawn.1 

It  may  be  urged  that  having  made  his  first 
rough  sketch  in  the  manner  which  came  most 
natural  to  him,  the  architect  could  easily  have 
changed  it  when  once  he  had  begun  his  work- 
ing drawings.  But  Leonardo  would  not  have 
considered  the  problem  in  that  light.  He  was 
no  mere  slave  to  precedent.  He  had  begun 
by  drawing  the  left-handed  spiral  which  came 
instinctively  to  the  left-handed  draughtsman. 
It  interested  him  to  notice  the  difference  from 
the  usual  form,  and  he  went  on  with  his 
rarer  form  deliberately,  carefully  investigating 
whether  it  was  better  than  the  common  style. 
As  we  look  at  the  turn  of  the  steps  now,  we 
realise  that  they  move  upward  in  the  same 
direction  as  the  hands  of  a  watch  moves  for- 
ward  as  it  lies  upon  a  table,  "  through  the 

1  The  fragments  brought  together  on  this  plate  show  also 
his  habitual  method  of  shading  from  left  to  right,  and  I 
have  given  his  right-handed  signature  in  the  same  place  in 
order  that  it  may  be  contrasted  with  the  far  firmer  and 
clearer  writing  done  by  his  left  hand  on  the  opposite  corner 
of  the  plate. 


176         THE    SHELL   OF   LEONARDO     [chap. 

buttonhole,"  as  they  say  in  Lincolnshire.  It 
is  after  this  manner,  too,  that  fashion  has 
decreed  we  should  deal  a  hand  at  cards,  and 
that  superstition  has  ordered  us  to  pass  the 
Port.1  In  architecture  also,  this  arrangement 
produces  an  effect  of  hospitality  in  the  curve, 
for  a  host  could  walk  down  it  with  welcoming 
right  hand  outstretched  to  the  ascending  guest, 
who  was  in  his  turn  helped  on  his  ascent  by 
keeping  his  own  right  hand  on  the  side-rail, 
just  as  you  may  see  the  modern  athlete  keep 
his  right  side  inwards  as  he  runs  round 
the  track  at  Queen's  Club.  Certainly,  also, 
this  stair  is  easier  to  walk  up,  a  fact 
which  may  be  verified  by  practical  experience 
to-day. 

Right-handed  spirals  are  not  only  more 
common  in  Nature,  they  occur  more  often 
in    art,    because    the    average    right  -  handed 

1  In  1690  a  new  "Dictionary  of  the  Canting  Crew"  was 
published,  in  which  the  phrase  "  Catharpin-fashion  "  is  de- 
fined as  follows  : — "  When  People  in  Company  Drink  cross, 
and  not  round  about  from  the  Right  to  the  Left,  or  accord- 
ing to  the  sun's  motion."  The  word  "withershins,"  or 
"  widdershins,"  also  means  against  the  sun  (wither = against, 
shins= sun's),  and  to  go  round  a  church  from  left  to  right  (as 
you  face  the  chancel  from  within)  was  believed  to  give  the 
Devil  power  over  so  careless  a  traveller.  The  word  may  be 
connected  with  wiederschein  = to  reflect,  as  in  Virgil's  de- 
scription of  the  rainbow,  "Mille  trahit  varios  adverso  sole 
colores." 


x]  THE   DEXIOTROPIC   SHELL         177 

architect  had  not  cared  to  face  the  result 
that  they  involved  a  continual  turning  to  the 
left;  so  he  followed  precedent,  although  on 
a  left-handed  spiral  a  man  turns  easily  and 
naturally  towards  the  right  in  his  ascent.  So 
far,  then,  this  new  arrangement  must  have 
satisfied  Leonardo's  practical  sense  of  fitness. 
But  it  involved  carrying  out  the  same  idea  of 
reversal  in  its  entirety,  without  the  help  of 
any  previous  examples  in  the  district  to  guide 
him. 

Certainly,  if  it  was  a  shell  before  him  of 
which  he  was  thus  reversing  both  the  internal 
and  external  lines,  he  was  the  only  architect 
then  living  who  might  have  done  so  with  the 
knowledge  that  Nature  had,  in  one  example 
out  of  every  million,  done  the  same  before 
him.  One  of  these  rare  examples  he  may 
have  possessed  and  used,  but  it  is  more  prob- 
able that  he  did  not  have  before  his  eyes  so 
uncommon  a  dexiotropic  Voluta  as  that  which 
I  have  reproduced  in  figs.  54  and  57  ;  and  if 
he  did  not,  this  rare  shell,  shaped  by  some 
left-handed  angel  of  the  Ocean,  and  worshipped 
as  the  evidence  of  some  supernatural  presence, 
becomes  a  triumphant  vindication  of  his  skill ; 
for  when  its  reversed  lines  are  compared  with 
his  staircase,  they  will  be  found  exactly  to 
correspond  in  every  case.  Rare  as  the  sinistral 
single  spiral  is  in  architecture,  Leonardo's  par- 

M 


178        THE   SHELL   OF   LEONARDO     [chap. 

ticular  development  of  the  fourfold  sinistral 
spiral  is  unique;  and  it  is  significant  that 
the  double  interlacing  staircase  built  by 
Pierre  Trinqueau  in  1526.  close  at  hand 
in  Chambord  (see  fig.  41),  is  also  of  this 
same  rare  sinistral  form  which  had  but  just 
previously  been  built  by  the  Loire ;  in  tacit 
acknowledgment,  as  it  seems  to  me,  that 
no  single  stairway,  even  if  it  were  similarly 
reversed,  could  ever  compete  for  sheer  beauty 
of  construction  with  the  older  masterpiece  at 
Blois. 

To  Leonardo  the  revelation  of  spirality  thus 
so  triumphantly  manifested,  its  connection  with 
religious  doctrines,  and  the  value  of  its  sym- 
bolism, must  strongly  have  appealed.  As  we 
know,  he  investigated  many  of  the  forms 
it  took,  and  no  doubt  he  knew  far  more 
of  them  than  I  have  indicated  here.  He 
found  it  in  such  humble  instances  as  the  coil 
of  the  worm,  the  curve  of  the  snailshell,  the 
budding  of  the  fern.  Completed  in  the  Ionic 
capital,  arrested  at  the  bending-point  of  the 
acanthus-leaf  in  the  Corinthian,  it  became, 
he  saw,  a  primal  element  of  architectural 
ornament,  eloquent  with  many  meanings, 
representing  the  power  of  his  favourite 
waves  and  winds  in  Greek  building,  typifying 
the  old  Serpent  of  unending  Sin  in  Gothic 
workmanship. 


x]  THE   MISTRESS-ART  179 

For  him  science  was  the  handmaid  of  the 
imitative  and  creative  arts,  the  tool  by 
which  he  gave  reality  to  his  imaginations. 
His  work  was  the  healthy  manifestation  of  a 
strong  and  subtle  intellect ;  the  mixture,  and 
the  equipoise,  of  all  that  is  best  in  the  faculties 
of  man ;  and  this  is  why  his  creations  show 
that  elusive  quality  of  naturalism  mingled  with 
the  ideal,  of  analysis  with  emotion,  of  soul  with 
body.  In  him  the  artist  and  the  scientist 
dwelt  harmoniously  together,  worked  harmoni- 
ously. No  one  of  his  time  had  observed  so 
keenly ;  no  one  could  express  his  observations 
with  a  greater  realism.  But  his  art  was  no 
mere  servile  form  of  imitation.  He  could 
both  imagine  and  create,  because  he  had  an 
inexhaustible  material  from  which  to  mould 
fresh  forms.  "  Non  e  creatore  se  non  Iddio  ed 
il  poeta "  ("  God  and  the  poet  are  the  only 
creators")  said  Tasso.  But  only  an  intellect 
so  comprehensive  as  was  Leonardo's  could 
have  justified  the  greater  saying :  "  Natural 
Things  are  finite,  but  the  works  which  the 
Eye  can  order  of  the  Hand  are  infinite. "  One 
such  "work"  of  his  creative  imagination  did 
he  reserve  for  the  close  of  his  life,  and  for 
its  expression  he  chose  that  "  mistress-art," 
architecture,  to  which  all  the  other  arts  he 
knew  are  handmaids. 

Again  and   again  has  the  same  search  for 


180        THE   SHELL    OF   LEONARDO     [chap. 

the  subtle  and  elusive  causes  of  beauty  been 
taken  up.     It  has  attracted  minds  so  different 
as   Hume,   Bernouilli,   Burke,   and  Winckel- 
mann,  among  many  others.     Hogarth  left  us 
his  idea  of  it.     Professor  Goodsir  adopted  the 
logarithmic    spiral   as    a   kind   of  teleological 
chart   in   Nature's  beautiful  designs.     Taking 
Canon  Moseley's  investigations  as  his  text,  he 
tried  to  illustrate   their  logical  corollary  that 
the  form  and   law   of  growth   of  an   organic 
body  being  known,  its  form  at  any  future  time 
might   be   made    a    matter    of  mathematical 
elucidation.     Following   out  with  astonishing 
fidelity  the  line  of  investigation  laid  out  by 
Leonardo    da    Vinci    three   centuries   before, 
Professor   Goodsir   asked   when   it   would   be 
possible,  by  ascertaining  the   accurate   shape, 
form,     and     proportion    between    the    parts, 
organs,   and   whole   body   of  any   animal,   to 
advance  anatomical  study  geometrically.     One 
of  his  most  enthusiastic  disciples,  D.  R.  Hay 
("  On  the   Human   Figure,"    1849  ;  "  Natural 
Principles  of  Beauty/'  1852  ;  "  The  Science  of 
Beauty,"  1856),  examined  the  geometric  out- 
line of  the   human   body,  just   as   Leonardo 
is  said  to  have  done  when  the  Aphrodite  of 
Praxiteles  was  discovered,  and  produced  a  cer- 
tain harmonic  proportion,  by  following  which 
a  correct  anatomical  outline  could   be  drawn 
from  a  mathematical  diagram.     What  Goodsir 


x.]  THE   CURVE   OF   GROWTH  181 

sought  for  all  his  life  was  some  physiological 
law  ruling  the  form  and  growth  of  organisms 
as  gravitation  is  held  to  prevail  in  the  physical 
world.  If  from  the  geometric  curves  of  the 
planets'  orbits  Newton  deduced  the  law  of 
the  force,  said  he,  may  we  not  learn  "  the  law 
of  the  force"  in  natural  objects  also  when 
we  have  got  their  mathematical  forms  ? 
It  may  be  very  long  before  we  do  so, 
because  very  few  biologists  are  mathemati- 
cians as  well.  But  if  ever  this  does  come 
to  pass,  Canon  Moseley's  paper  will  be  taken 
as  the  beginning  of  a  new  epoch  in  natural 
science. 

Professor  Goodsir  considered  that  biology 
owed  its  progress  to  the  study  of  final  causes, 
to  the  study  of  the  remarkable  adaptation 
of  structures  to  particular  functions.  This 
is  not  the  most  fertile  mode  of  procedure  in 
physical  or  chemical  investigations,  owing  to 
the  difference  between  organised  and  in- 
organised  bodies.  For  each  individual  organ- 
ism forms  a  system  in  which  the  reason  why 
its  parts  are  adapted  to  each  other  may  be 
studied.  But  it  is  impossible  to  put  the  Solar 
System  under  our  eye  and  examine  it  in  order 
to  explain  the  Sun.  It  is  noticeable,  however, 
that  Newton  showed  in  his  "Principia"  that 
if  attraction  had  generally  varied  as  the  inverse 
cube  instead  of  as  the  inverse  square  of  the 


182         THE   SHELL   OF   LEONARDO     [chap. 

distance,  the  heavenly  bodies  would  revolve, 
not  in  ellipses,  but  in  logarithmic  spirals,1 
rapidly  diffusing  themselves  and  rushing  off 
into  space.  If  therefore,  asked  Goodsir,  the 
law  of  the  square  is  the  law  of  attraction,  is 
the  law  of  the  cube2  the  law  of  production, 
and  is  the  logarithmic  spiral  the  manifestation 
of  the  law  which  is  at  work  in  the  increase 
of  organic  bodies  ? 

The  process  by  which  such  results  as  those 
shown  in  the  "Principia"  must  be  reached 
may  be  described  as  two  steps,  the  first  being 
the  hypothesis  (based  on  the  purely  abstract 
conception  of  perfect  motion)  that  the  motion 
of  a  planet  was  like  that  of  a  ball  swung  on 
the  end  of  a  string ;  the  second  step  is  when 
Science  discards  the  hypothesis,  and  uses 
it  merely  to  investigate  the  properties  of  a 
planet's  motion.  This  is  the  process  that  has 
been  exemplified  in  the  discovery  of  the  law 
of  light  and  heat,  or  in  the  hypothesis  which 
is  based  upon  the  abstract  conception  of  a 
perfect    liquid.       Clearly,    there    can    be   no 

1  It  is  worth  considering  in  this  connection  that  the 
growth  of  systems  seems  to  be  expressed  in  the  spiral 
nebulae  discovered  by  Lord  Rosse,  as  opposed  to  the 
circling  of  completed  weights  in  the  case  of  perfect  planets 
which  follow  a  fixed  orbit,  owing  to  the  unvarying  law 
of  gravity. 

2  "  The  law  of  the  cube,"  that  is,  the  law  of  the  cell 
also. 


x]  CHURCH'S   THEORY  183 

objection,  as  Mr  Church  points  out,  to  the 
application  of  a  mathematical  conception  in 
itself  either  to  phyllotaxis  and  the  arrange- 
ment of  leaves  upon  a  stalk,  or  to  conchology 
and  the  growth  of  the  Nautilus.  Everything 
in  nature  is  capable  of  mathematical  expression 
if  the  conditions  are  only  sufficiently  well 
known ;  the  real  difficulty  is  to  select  a 
fundamental  conception  which  will  admit  of 
modification  when  new  factors  are  introduced. 
In  other  words,  if  the  genetic  spiral  be  regarded 
mathematically  as  winding  to  infinity,  and 
being  engaged  in  the  production  of  similar  mem- 
bers, it  can  only  be  represented  by  the  loga- 
rithmic spiral  which  makes  equal  angles  with 
all  radii  vectores.  "  Eadem  mutata  resurgit." 
This  spiral,  representing  the  laws  of  mathe- 
matical asymmetrical  growth  around  a  point, 
constitutes  in  Hydro-Dynamics  the  curves 
of  spiral- vortex  movement,  and  its  application 
to  magnetism  has  been  fully  investigated  by 
Clerk  Maxwell. 

From  this  last  point  Mr  Church  is  now 
working  towards  the  proof  of  a  hypothesis 
which  he  has  not  fully  published ;  but  he 
clearly  thinks  that  the  distribution  of  living 
energy  follows  identical  lines  with  those  of 
electrical  energy,  for  example,  and  that  a 
phyllotaxis  diagram,  or  (as  I  should  add)  the 
plan  of  a  Nautilus,  is  comparable  to  electrical 


184         THE   SHELL   OF  LEONARDO      [chap. 

lines  of  equipotential.1  The  theory,  if  correct, 
would  be  fundamental  for  all  forms  of  growth, 
though  it  could  be  more  easily  observed  in 
plant-protoplasm  than  in  animals.2 

1  If  this  hypothesis  be  correct,  it  may  form  a  very  im- 
portant factor  in  such  experiments  as  those  reported  by 
Mr  A.  B.  Plowman  in  the  Harvard  Botanic  Garden,  on  the 
relations  of  electricity  to  plant-growth,  or  in  such  researches 
as  those  of  Professor  Lemstrom  of  Helsingfors. 

2  Mr  Church's  further  statements,  being  somewhat  too 
technical  for  the  ordinary  reader,  though  of  extreme 
importance  to  the  theory  mentioned  above,  are  here  quoted 
in  a  footnote  from  his  "  Note  on  Phyllotaxis  "  (1901). 

"  The  possibility  that  the  contact  parastichies  may  be 
also  not  only  log-spirals  but  log-spirals  which  intersect 
orthogonally,  and  thus  plot  out  a  field  of  distribution  of 
energy  along  orthogonally  intersecting  paths  of  equal 
action,  is  so  clearly  suggested  that  it  may  at  once  be 
taken  as  the  groundwork  of  a  theory  of  phyllotaxis  more  in 
accordance  with  modern  lines  of  thought.  ...  It  is 
difficult  to  avoid  the  conclusion  that  the  logarithmic  spiral 
construction  gives  the  true  key  to  the  problem,  and  that 
the  whole  subject  thus  becomes  a  question  of  the 
mechanical  distribution  of  energy  within  the  substance  of 
the  protoplasmic  mass  of  the  plant-apex  :  that  phyllotaxis 
phenomena  are  the  result  of  inherent  properties  of 
protoplasm,  the  energy  of  life  being  in  fact  distributed 
according  to  the  laws  which  govern  the  distribution  of 
energy  in  any  other  form  :  and  that  the  original  orthogonal 
planes,  the  relics  of  which  survive  in  the  contact 
parastichies  of  the  system,  represent  the  natural  con- 
sequence of  a  mechanical  system  of  energy-distribution 
directly  comparable  with  that  which  produces  the  ortho- 
gonal intersection  of  cell-walls  at  the  moment  of  their  first 
formation."  .  .  .     "The    logarithmic    spiral    theory,"   he 


x.]  THE   UNKNOWN   FACTOR  185 

It  will  be  seen  that,  in  all  efforts  to  define 
a  natural  object  in  mathematical  terms,  we 
come  to  a  point  at  which  our  knowledge  of 
the  involved  factors  ceases.  The  Nautilus  is 
almost  a  logarithmic  spiral,  but  not  quite. 
Nor  can  a  phyllotaxis  diagram,  as  Mr  Church 
admits,  ever  show  that  the  plant's  growth  is 
mathematically  correct.  All  that  can  be  said 
is  that  the  logarithmic  spiral  is  as  near  as  we 
can  get  in  mathematics  to  an  accurate  de- 
finition of  the  natural  phenomena.  To  this 
same  stopping-place  the  mathematician  is  also 
brought  when  he  tries  to  express  beauty  in 
terms  of  measurement.  In  other  words,  the 
baffling  factor  in  a  natural  object  is  its  life, 
its  organic  growth.  The  baffling  factor  in 
a  masterpiece  of  creative  art  is  its  beauty,  a 
quality  as  essential  and  as  intangible  as  life. 
This  means  therefore  that  growth  cannot  be 
wholly  expressed  by  algebra  or  trigonometry, 

concludes,  "  is  so  far  then  the  logical  outcome  of  Sachs* 
theory  of  the  orthogonal  intersection  of  cell-walls,  and 
represents  therefore  another  special  case  of  the  distribution 
of  energy  along  planes  of  '  equipotential.' " 

The  symbolism  of  the  spiral  form  of  ornament  originally 
taken  from  the  lotus  (see  p.  49)  therefore  receives  a  striking 
confirmation  of  its  power  and  meaning;  and  the  occurrence 
of  the  logarithmic  spiral  in  such  minute  organisms  as  the 
microscopic  Stentor  coeruleus  indicates  how  widely  this  mar- 
vellous curve  can  be  applied  to  a  consideration  of  living 
growth  (p.  73). 


186        THE   SHELL   OF  LEONARDO      [chap. 

though  these  may  help  us  to  appreciate  and 
describe  the  phenomena  we  examine.  It 
means  also  that  a  thing  constructed  merely  by 
rule  and  thumb  and  mathematics  must 
inevitably  fall  short  of  perfect  beauty.  For 
perfect  beauty,  like  natural  growth,  implies 
irregular  and  subtle  variations. 

By  this  path  we  may  perhaps  reach  some 
more  intelligible  explanation  of  that  vague 
but  most  important  quality — "good  taste." 
It  is  born  in  some  men  and  unknown  by 
others.  It  can  be  widely  distributed,  or  the 
life  of  ancient  Hellas  becomes  an  unintelligible 
miracle.  It  can  be  lost  in  just  as  large  a 
measure,  or  most  modern  architecture  would 
be  a  nightmare,  from  which  our  waking 
moments  would  be  free.  It  has  a  definite 
relation  to,  and  a  keen  sympathy  with,  the 
phenomena  of  life  and  growth  ;  so  it  must 
to  some  extent  partake  of  their  qualities. 
A  man  whose  vitality  is  strong,  whether  it 
be  physical  or  intellectual,  would  therefore 
be  likely  to  possess  it,  if  he  were  keenly  in 
touch  with  Nature,  if  he  abhorred  artificial 
rules,  and  mathematical  or  mechanical  results. 
This  would  explain  both  its  general  prevalence 
in  ancient  Hellas,  and  its  general  absence  in 
an  age  wThen  machine-made  productions  have 
become  paramount ;  when  designers  trust  to 
mathematics  ;    when  the  public  object  to  any- 


x.]  THE   IONIC   VOLUTE  187 

thing  but  repetition.  One  of  the  chief  mani- 
festations of  "good  taste/'  then,  is  the 
appreciation  of  the  truth  that  beauty,  like 
life  and  growth,  depends  not  on  exact  copy- 
ing, but  on  those  subtle  variations  to  which 
the  scheme  of  creation,  as  we  know  it,  owes 
those  great  laws  of  the  origin  of  species  and 
the  survival  of  the  fittest. 

A  good  architectural  example  of  this  de- 
liberate and  subtle  variation,  which  was  the 
Greek  ideal  of  beauty,  may  be  found  in  the 
volute  of  an  Ionic  capital.  It  is  no  more 
mathematically  correct  than  the  lines  of  the 
Parthenon  are  mathematically  straight.  It 
is  beautiful  because  it  exhibits  just  those 
variations  which  are  observable  in  organic 
growth. 

The  ordinary  method  of  drawing  a  "  correct " 
volute  with  the  help  of  an  inverted  cone  is,  of 
course,  well  known,  and  results  in  a  mathe- 
matically exact  and  aesthetically  vapid  figure. 
But  Mr  Banister  F.  Fletcher  (in  the  Building 
News  for  22nd  August  1902,  p.  247)  has 
shown  that  a  shell  can  be  used  for  the  same 
purpose  (fig.  61).  Following  his  instructions, 
I  took  the  sinistral  whelk  mentioned  on  page 
90,  and  wound  a  piece  of  tape,  12  inches  long, 
round  its  spirals  from  its  apex  (E)  to  the  top 
of  the  opening,  leaving  a  little  of  the  tape  over 
to   hold   the   rest   in  position.     A  pencil  was 


188        THE   SHELL   OF   LEONARDO      [chap. 

attached  to  the  end  of  the  tape  touching  the 
apex.  Reversing  the  shell  so  that  it  stood 
perpendicularly  upon  its  apex  at  the  point 
marked  E  in  the  diagram  of  the  volute,  and 
keeping  it  fixed  on  that  point,  I  drew  the 
pencil  round  and  round  the  shell  in  the  gradu- 
ally increasing  curves  permitted  me  by  the 
gradual  unwinding  of  the  string.  The  volute 
reproduced  in  fig.  61  is  the  result.  The  shell 
used  was  exactly  contained  in  a  rectangular 
space  4r^  inches  long  by  2\  inches  wide.  It 
produced  a  spiral  measuring  lOf  inches  across 
from  E  to  A.  Though  both  shell  and  volute 
are  reduced  to  suit  the  size  of  these  pages,  the 
relative  proportions  remain  the  same.  It  will 
be  noticed  that  the  Chrysodomus  antiquus 
employed  is  a  common  specimen  of  a  sinistral 
shell,  and  has  therefore  produced  the  left-hand 
volute  of  the  capital.  The  right-hand  volute 
can  be  similarly  produced  from  a  common 
right-handed  whelk. 

This  method,  though  mechanically  per- 
formed, actually  reproduces  those  proportions 
of  an  Ionic  volute  which  owe  none  of  their 
charm  to  mathematics ;  and  whether  the 
ancient  Greeks  used  a  shell  or  not  in  making 
their  designs,  it  is  very  significant  that  the 
beauty  of  their  workmanship  should  exhibit 
so  exact  a  harmony  with  the  lines  of  an  organic 
growth   that  are   nearly,    but   not   quite,  the 


§> 

^ 


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o 

Ll 


o 


2 


e 


x.]  PRINCIPLES   OF  BEAUTY  189 

curves  of  a  mathematical  spiral.     It  is  in  this 
subtle  difference  that  their  charm  consists. 

So  strongly  did  Goodsir  himself  believe  in 
the  correctness  of  the  theory  which  Mr 
Church  is  now  developing  on  original  and 
progressive  lines,  that  on  his  grave  in 
Edinburgh,  where  a  medallion  portrait  is  now 
fixed,  he  originally  ordered  the  logarithmic 
spiral  to  be  sculptured,  which  represented  to 
him  the  fundamental  principle  of  beauty  and 
of  growth  in  nature.  Pettigrew  and  Francis 
Darwin  have  done  much  towards  the  in- 
vestigation of  spiral  formations  in  Nature; 
and  to  many  another  besides  Professor 
Goodsir's  pupil  has  the  same  idea  appealed. 
But  not  one  of  all  of  these  has  left  such  visible 
monuments  of  insight  and  creative  power  as 
the  Leonardo  who  saw  the  same  problems 
both  in  Nature  and  in  Art  so  long  before  them. 

"Majestati  Naturae  Par  Ingenium."  We 
have  not  yet  said  the  last  word  on  that  theory 
of  flight  he  studied  from  the  wings  of  birds 
before  the  fifteenth  century  was  gone.  We 
know  very  little  more  than  he  has  written 
of  the  mysterious  forces  which  shape  the 
structures  of  waves,  of  reeds,  of  animals,  of 
shells.  We  are  still  groping  after  those 
fundamental  laws  he  sought,  which  existed 
"before  the  fair  flowers  were  seen,  or  ever 
the   movable  powers  were  established,  before 


190        THE   SHELL   OF  LEONARDO  [chap.  x. 

the  innumerable  multitude  of  angels  were 
gathered  together,  or  ever  the  heights  of  the 
air  were  lifted  up."  We,  too,  must  look 
beyond,  as  he  looked  long  ago  towards  the 
stars,  moving  in  the  sky  "  to  their  own  natural 
home,  which  they  enter  unannounced  as  lords 
that  are  certainly  expected,  and  yet  there  is 
a  silent  joy  at  their  arrival." 


<^ 


o 


o 


2 


g 


INDEX 


INDEX 


Abbey  of  Thelema,  143 

Accatabriga,  150 

Accidents,  68 

Africa,  48 

Air  tubes,  117 

Airy's  spirals,  130 

Alaska,  48 

Alaskan  Bighorn,  81 

Alberti  (Leon  Battista),  103 

Aleutian  Isles,  48 

Amalekites,  37 

Amboise,  146,  149,  152, 157, 159, 

173 
Ambrosian  Library,  149 
Ammonite,  42,  91,  93,  124,  126, 

157 
Amory  valley,  48 
Ampelopsis  hederacea,  67 
Amphidromus,  90 
Amphidromus  perversus,  89 
Amsterdam,  47 
Angora,  80 
Antelopes,  79,  86 
Antonio  da  Vinci,  150 
Apennines,  22 
Aphrodite,  180 
Aploceras,  93 
Arab,  48 
Arbela,  36 
Architecture,  8 
Archimedes,  157 
Arezzo,  108 
Argali,  81 

Argonauta  Argo,  124 
Arm  supports,  87 
Assyrian,  48 
Asymmetry,  100 
Atlas  (Mount),  22 
Augur-shell,  33 
Auricula  auris  midae,  158 


N 


Australasia,  125 
Azay  le  Kideau,  140 

Baikal  (Lake),  91 

Balfour,  (Henry),  47 

Barbour  (Professor),  60 

Barrande,  93 

Barton  beds,  6, 173 

Bayard,  147 

Bean,  62,  66 

Bedouin,  99 

Belsay,  139 

Belshazzar,  35 

Beltrami,  11 

Bengal,  45 

Benjamin  of  Tudela,  111 

Benjamites,  37 

Berkshire,  65 

Bernouilli,  24, 124, 180 

Bighorn,  81 

Billingsgate,  89 

Blarney  Castle,  139 

Blois,  4,  9,  98,  145, 157, 162, 173 

Blois  (old  staircase),  144 

Blois  (Chateau),  132, 141 

Bologna,  110 

Bonanno,  109 

Bonnet,  55,  69,  72 

Boreau,  150 

Borneo,  46 

Brachiopods,  86 

Bramante,  151 

Brantome,  143 

Braun,  70 

Brazil,  56 

Bronze  Age,  45 

Browne   (Sir  Thomas),   19,   23, 

37 
Bryony,  67 
Buccinum  undatum,  89 

193 


194 


INDEX 


Buckland  (Frank),  41 
Buddhist,  48 
Buffaloes,  86 
Burke,  180 
Bushbuck,  76 
Byzantine,  48,  100, 106 

Cesar  Borgia,  147, 148 
Calandrini,  70 
CalcispongiaB,  52 
Calderon  (George),  49 
Cambrensis  (Giraldus),  34 
Campanile  of  Pisa,  96, 108 
Canterbury  Cathedral,  30 
Cape  of  Good  Hope,  125 
Capra  falcon eri,  80 
Capra  walie,  83 
Carnauba  Palm,  56 
Catharpin,  176 
Catherine  de  Medici,  171 
Celts,  36 

Central  column  (origin),  135 
Ceritheum  giganteum,  119 
Cerithium  Portlandicum,  33 
Ceropegia  Gardnerii,  63 
Cestracion  philippi,  75 
Chaldee,  35 
Chambord,  143,  178 
Chank  shell,  44 
Charles  V.,  134,  159 
Charles  VIII. ,  159 
Charlotte  d'Albret,  148 
Chartres,  97, 162 
Chenonceaux,  140 
Cher,  156 
Chester,  153 
Chesterfield,  96 
Chestnut,  57 
Chevreuil,  24 
Chichly,  107 
Chinon,  147 
Chippendale,  113 
Choanomphalus,  91 
Chrysodomus  antiquus,  90,  188 
Church    (A.    H.),    70,    92,    124, 

183 
Clausilia  laminata,  128 
Clerk  Maxwell,  183 
Clifford  (Professor),  21, 130 
Climbing  plants,  62 
Clos-Luce,  48 
Cloux,  147, 149 


Clymenia,  92 
Cobus  unctuosus,  78 
Cochlea,  75 

Cochliodus  contortus,  42 
Codex  Atlanticus,  11 
Codice  Atlantico,  149 
Coffin  screw,  32 
Cokerell,  104 
Collar-day,  36 
College  de  Montaigu,  144 
Coloration,  85 
Columella  muscle,  120 
Columella  plaits,  115 
Columna  flammea,  89 
Convolvulus,  59,  62 
Copenhagen,  96 
Copernicia  Cerifera,  56 
Copernicus,  23 
Corea,  125 
Corkscrew,  31 
Cormack  McCarthy,  139 
Cornish  (Vaughan),  156 
Cowry,  45 
Crete,  45,  83 

Crioceras  bifurcatum,  91 
Crypt  of  Canterbury,  31 
Cumberland,  139 
Curves  in  building,  104 
Cuvier,  22,  74 
Cyclamen,  55,  152 
Cylindrella,  92 
Cymbiola  tuberculata,  120 
Cymbium,  119,  167 
Cypraea  annulus,  45 
Cypraea  moneta,  45 
Cypriot,  48 
Cyrtoceras,  93 

Dacca  44 

Dacre  Castle,  139 

Daemonelix,  60 

D'Alembert,  24 

Darius,  36 

Darwin,  16,  22,  62,  65,  67,  68,  70, 

118 
Darwin  (Francis),  62 
Date  Palm,  57 

Deluge  (Scriptural),  12,  22,  156 
Devil,  46 

Devil's  Corkscrews,  60 
Devonshire,  55 
Dexiotropic,  87 


INDEX 


195 


Dexiotropic  Voluta,  177 
Dextral  helix,  27 
Diatoms,  52 
Domestication  85 
Donaldson,  104 
Douglas  (the  Black)  139 
Dover,  35 
Driving,  27 
Druids,  36 
Drummond  (Dr),  60 
Dunstan  (Professor),  173 
Duval,  11 

Eclipse  (racehorse),  127 
Eglantine,  152 
Egypt.  45,  48,  59,  99 
Elands,  78 
Elasmobranch,  42 
Electricity,  75 
Elephant,  41 
Elgin  (Lord),  104 
Entasis,  104 
Eocene,  173 

Equiangular  spiral,  122 
Etienne  de  Loup,  148 
Euclid,  113 
Euglena  oxyuris,  74 
Euglena  spirogyra,  74 
Evans  (Arthur),  45 
Evelyn,  108 
Evolution,  70 
Eyestone,  126 

Felixstowe,  51 

Fencing,  27,  38 

Fiesole,  95,  160 

Flanders,  141 

Fletcher,  MrB.R,  187 

Flight  of  birds,  153 

Floral  diagrams,  59 

Florence,  109 

Florence  Court,  60 

Flying  (Treatise  on),  15 

Fossil  twisters,  60 

Fra  Giocondo,  156 

Framlingham,  97 

Francesco  Sforza,  148 

Francis  1, 109, 141,  143,  145, 147, 

148,  150 
Frankfort,  96 
Freeman  (Professor),  121 
Fresnel.  130 


Friston  Tower,  140 
Fusus  antiquus,  51 
Fyvie,  139 

Galileo,  17 

Garisenda,  110 

Gaudry  (Albert),  92 

Gelnhausen,  96 

Geymuller  (Baron  de),  151 

Gideon,  37 

Gilbert,  172 

Gioconda  (La),  156 

Goats,  79 

Goethe,  19,  70,  110 

Goodsir    (Professor),    124,    127, 

180, 181, 189 
Goodyear    (Professor),    48,    101, 

105,  106 
Goniatites,  92 
Gothic,  100,  101,  108 
Gothic  Eevival,  102 
Goujon  (Jean),  174 
Govi,  11 
Greeks,  48 
Greek  builders,  102 
Gremsmuhlen,  129 
Guglielmo,  109 
Gulf  of  Guinea,  89 
Gyroceras,  93 

Hair,  39,  85 

Haliotida  Cunninghamii,  125 
Haliotida  gigantea,  125 
Haliotida  midse,  125 
Hamilton  (Sir  W.  R),  130 
Hampshire,  173 
Hand-rail,  141 
Hand-writing,  13 
Harpula  fulminata,  120 
Harvard,  184 
Hay  (D.  B.),  180 
Heart  fibres,  75 
Heart  (valves  of),  22 
Helicoprion,  42 
Helicteres  ixora,  50 
Hellenic  art,  186 
Helmholtz,  21 
Helsingfors,  184 
Hepplewhite,  113 
Heredity,  70 
Hertford  College,  138 


196 


INDEX 


Heteronymous,  78 

Hexacoralla,  52 

Highland  Earn,  77,  81 

Hindu,  44 

Hofer,  105 

Hogarth,  180 

Holbein,  38 

Holland,  141 

Holmes  (DrO.  W.),  126 

Holstein  (Eastern),  129 

Homonymous,  78 

Honecort  (Wilars  de),  102 

Honeysuckle,  62 

Hops,  49,  62,  63,  65 

Horse-chestnut,  57 

House  of  Commons,  140 

Houssaye  (Arsene),  149 

Humboldt,  17 

Hume,  180 

Hungary,  83 

Hunter  (William),  153 

Huxley,  16 

Ibex,  83 

Iceland  spar,  130 
He  de  France,  101 
II  Moro,  147 
Indre,  147 
Infusoria,  125 
Ionic  Volute,  187 
Ipswich,  140 
Ireland,  139 
Irish  torques,  34 
Irritability,  64 
Isabella  d'Este,  151 
Isle  of  Bourbon,  57 

Jaffna,  44 
Japanese,  33 
Jew's  ear,  50 
Jones  (Inigo),  103 
Joursanvault  (Baron  de),  173 

Kepler,  4 
Kew,  56 

Kirchhoffer,  28,  38 
Koninckina  leonhardi,  87 
Koodoo,  76 
Kumatology,  156 

Lady's  Tresses,  55 
Lamarck,  70 


Lamona,  22 

Lanistes,  51,  90 

La  Tremouille,  147 

Leaning  Tower,  109 

Leda,  157 

Lee-Metford,  32 

Left-handedness,  37,  175 

Left-handed  writing,  175 

Leiotropic,  32,  87 

Lemstrom,  184 

Leonardo  da  Vinci,  4, 10,  38, 114, 

132,  145,  146,  150,  151 
Lepus  cuniculus,  158 
Leslie  (Sir  John),  121,  125 
Ley  den,  47 
Libri,  11 
Limacina,  90 
Lincolnshire,  140,  176 
Lithuanian,  49 
Lizards,  75 
Loasa  aurantiaca,  62 
Loches,  147 
Logarithmic  curve,  92 
Logarithmic  spiral,  71,  122,  183, 

184 
Loire,  146,  149,  156 
Lombardy,  24, 151,  160 
London,  132,  153 
Lotos,  47,  49 
Louis  XI.,  148 
Louis  XII.,  145, 148 
Louvre,  134,  149 
Ludovico  Sforza,  147 
Lyell,  22 
Lyme  Regis,  124 
Lynn,  140 

Macon,  149 

Macroscaphites  gigas,  92 
Macroscaphites  ivanii,  92 
Madagascar,  57 
Madrid,  143 
Maison  Carree,  105 
Malay,  46,  47,  48 
Malpighi,  117 
Mammal,  75 

Manderville  (John  de),  21 
Manlius  Torquatus,  36 
Mansion  House,  112 
Manuscripts  (Leonardo's),  13 
Maori,  46 
Marey  (Professor),  154 


INDEX 


197 


Marey  (E.  J.),  74 

Marignano,  148 

Markhor,  77,  84 

Martello  towers,  139 

Medinet  Habou,  104,  105 

Mediterranean,  89 

Meladromus,  90 

Melanesia,  46 

Melia,  93 

Melzi  (Francesco),  148, 149 

Merignac,  38 

Merino  Ram,  81 

Metamorphosis  of  leaves,  70 

Meyer  (Hermann),  75 

Michelet,  19 

Middleton  Tower,  140 

Milan,  108,  148,  173 

Milan,  Duke  of,  151 

Milanesi,  150 

Minos,  45 

Miratesta,  89 

Mitra  papalis,  27,  97 

Mohammedan,  48 

Mona  Lisa,  169 

Montreal,  60 

Montrichard,  157 

Moore  (Julian),  101,  107 

Moore  (J.  E.  &),  52 

Moorish,  99 

Morantin,  149 

Moseley  (Canon),  122,  127, 180 

Miintz,  11 

Miiller  ( Johann),  17 

Muller-Walde,  11 

Mycenae,  47 


Nautiloceras,  93 
Nautilus,  91,  92,   111, 

123, 125,  126, 183 
Naples,  36 
Narwhals,  39 
Nature  (finite),  18 
Nebulae  (spiral),  76 
Neottia  spiralis,  55 
Nepenthes,  117 
Newel,  136 
New  Guinea,  46 
Newton,  71, 181 
New  Zealand,  58 
Nicobar  Islands}to57 
Nile,  48 
Niobrara  River,  60 


115,  122, 


Norfolk,  140 
North  Berwick,  139 
North  Sea,  51 
Northumberland,  139 
Nunney  Castle,  140 
Nutation,  63 
Nyassa,  51 

Oblique  plans,  106 

Oncyloceras  spinigerum,  91 

Onion,  59 

Open  staircase,  166 

Operculum,  90, 122,  126 

Ophidioceras,  93 

Optically  neutral,  131 

Orchid,  55 

Orientals,  34 

Orthoceras,  93 

Orton  Scar,  35 

Ovis  nivicola,  86 

Owen,  91 

Oxford,  113, 138 

Pacioli  (Fra  Luca),  13 

Palaeolithic,  37 

Palais  de  Justice,  96 

Palazzo  Contarini,  95,  136 

Palissy  (Bernard),  22 

Pamir,  81 

Pandanus  millore,  57 

Pandanus  sylvestris,  57 

Pandanus  utilis,  57 

Pandanus  vandermeschii,  57 

Paris,  113, 144 

Parthenon,  100,  104, 105,  106 

Pascal,  24 

Passion  flower,  62 

Pasteur,  131 

Patterns,  47 

Pa  via,  151 

Peas,  62 

Peels  (Border),  139 

Pelseneer,  90 

Pennethorne,  104,  105 

Penrose,  106 

Penrose  (F.  C),  105 

Persians,  35 

Peru,  46 

Petersburg,  42 

Pettigrew,  75 

Pharaoh's  serpents,  41,  88 

Phoenix  dactylifera,  57 


198 


INDEX 


Phryganeida,  74 

Phyllotaxis,  69,  183,  184 

Physa  fontinalis,  89 

Physa  heterostropha,  89 

Piedmont,  160 

Piero  da  Vinci,  150 

Pine  Ridge,  61 

Pinus  smithiana,  55 

Pir  Panjal,  80 

Pisa,  96,  108, 109 

Pisa  Baptistery,  110 

Pisa  Campanile,  111 

Pisa  Cathedral,  110 

Piumati,  11 

Plaits  on  columella,'  118 

Planorbis,  90 

Plants,  54 

Pliny,  21 

Plowman  (A.  B.),  184 

Po  (river),  22 

Polarised  light,  130 

Pompeii,  36,  137 

Pompholyx,  91 

Portland  screw,  33 

Poulton  (Professor),  85 

Praxiteles,  180 

Prat,  107 

Prentice's  Pillar,  29,  96,  144 

Pritchard  (Eric),  74 

Quadruple  helix,  163 
Queen's  Club,  176 

Rabbits,  41,  62 

Rabelais,  143 

Ralph,  Lord  Cromwell,  140 

Rata,  57 

Ravaisson-Mollien,  11 

Ravenna,  110, 

Raymond  du  Temple,  135 

Red  Crag  Sea,  51 

Renaissance,  102, 108- 

Revett,  104 

Revival  (Gothic),  102 

Richter,  11, 150 

Rocky  Mountains,  31,  61 

Rodin,  20 

Roman  screws,  137 

Rome,  47 

Romorantin,  151 

Rosse  (Lord),  76, 182 

Rosslyn,  29 


Rouen,  96,  106 
Rundthor,  96 
Ruskin,  16,  111,  121 

Sabachnikoff,  11, 155 

Sabba  da  Castiglione,  151 

Sabella,  74 

Sabella  unispira,  74 

Saint-Bel  (M.  Vial),  127 

San  Domenico,  95 

San  Paternian,  95 

Sankho,  43 

Saone,  149 

Santa  Maria  della  Grazie,  151 

Sant'  Ambrogio,  108 

Sauldre,  149 

Scala  del  Bovolo,  6,  95,  96 

Scala  della  conchiglia,  6,  95 

Scalaria  scalaris,  6,  95, 123 

Schaubert,  105 

Schimper,  70 

Schliemann,  43,  47 

Scotland,  139 

Screw-like  flight,  154 

Screw-palm,  57 

Screws,  32 

Screwstone,  33 

Sea-bean,  126 

Seailles,  11 

Septuagint,  35 

Shark's  egg,  75 

Shark's  intestine,  158 

Shavings,  33 

Shell  growth,  87 

Shells,  50 

Shells  (carved),  170 

Sheraton,  113 

Siliquaria,  91 

Simroth,  90 

Sinistral  helix,  28 

Sinistral  shells,  51,  89 

Sinistral  spiral,  174 

Sinistral  spiral  (fourfold),  178 

Sinistral    spirals    (interlacing), 

178 
Siphuncle,  91 
Situtunga,  84 
Skate,  42 
Smilax  aspera,  66 
Smoke  spirals,  152 
Solarium  maximum,  6,  94 
Somersetshire,  140 


INDEX 


199 


Spencer  (Herbert),  74 

Spiral  curve,  78 

Spiral  formations,  26 

Spiral  forms  of  water,  156 

Spiral  horns,  76 

Spiral  nebulae,  76 

Spiral  staircase  (origin),  132 

Spiral  Theory,  69 

Spiral  tubes,  116 

Spiral  twist,  78 

Spira  mirabilis,  124 

Spirialis,  90 

Spirifer  mucronatus,  87 

Spirostomum  ambiguum,  73 

Stein,  73, 125 

Stentor  coeruleus,  73,  125 

Stent  or  igneus,  73 

Stentor  multiformis,  74 

Stentor  polymorphus,  73 

Stentor  Roeselii,  73 

Stephanoceratidae,  91 

St  Florentin,  149 

St  Germain-en-Laye,  150 

St  John  the  Baptist,  149 

St  Mark's,  108 

Stone  Age,  46 

St  Ouen,  106 

St  Paul's,  107 

Strassburg,  110 

Streets,  113 

Stuart,  104 

Style,  53 

Sulieman  markhor,  84 

Sweden,  47 

Symmetrophobia,  109 

Tanganyika,  51 
Tantallon  Castle,  139 
Tasso,  179 
Taste,  186 

Tattershall  Castle,  140 
Taurotragus  oryx,  78 
Teeth,  42 

Telescopium,  91, 160 
Telescopium    telescopium,     98, 

119,  161 
Tendrils,  66 
Terebra  maculata,  33 
Terebra  semiplicata,  33 
Thebes,  104 
Torques,  34 
Torsion,  65,  68 


Touraine,  143, 161 

Tours,  97,157 

Tower  of  London,  136 

Tracheae,  116 

Tragelaphus  angasi,  79 

Tragelaphus  spekei,  84 

Travancore,  43, 164 

Trochus,  127 

Troy,  43 

Turbinella  fusus,  120 

Turbinella  pirum,  44,  119 

Turbinella  rapa,  44 

Turbine  shells,  122 

Turbo  marmoratus,  126  * 

Turbonilla,  91 

Turbo  olearius,  127 

Turf  (English),  128 

Turner  (Sir  William),  127 

Turritella,  160 

Turrilites  catenulatus,  89 

Turrilites  costatus,  89 

Turritella  lentiginosa,  119, 158, 

162 
Tuscany,  160 
Tuticorin,  44 
Two-fifth  spiral,  69 

Ultra-dextral,  90 
Ultra-sinistral,  91 
Uniform  growth,  71 
Uzielli,  11 

Vasari,  109,  150 

Venice,  108,  111,  160,  162 

Venturi,  11 

Victoria  Nyanza,  51 

Vienne,  147 

Viollet  le  Due,  136,  142, 144 

Vishnu,  43 

Vitruvius,  102,  104 

Voluta  (dexiotropic),  177 

Voluta  musica,  120, 162 

Voluta  pacifica,  119 

Voluta  scalaris,  6 

Voluta  solandri,  119 

Voluta   vespertilio,   5,   89,   119, 

162, 164, 167,  173 
Volute,  Ionic,  187 
Von  Mohl,  70 
Von  Thering,  90 
Vorticella,  74 


200 


INDEX 


Walking-sticks,  34 

Wallachian  sheep,  83 

Wantage,  107 

Ward  (Rowland),  84 

Washington,  36,  47 

Waterbuck,  78 

Water-lily,  58 

Wax  palm,  56 

Weldon  (Professor),  128 

Westminster  Abbey,  49,  107 

Whelk,  90, 187 

Wherry  (Dr),  40,  64,  67,  76,  86 

Whistler,  8 

White  River,  60 

Wilkins,  104 

William  of  Waynflete,  140 


Wilson  (Sir  Daniel),  37 
Winchester  (Bishop  of),  140 
Winckelmann,  180 
Windsor,  155 
Withershins,  176 
Wren,  108 

Wren  (Sir  Christopher),  107 
Wyndham  (Rt.  Hon.  Geo.),  20 

Yakoots,  48 
Yew,  59 


Zeuglodon,  75 

Zulus,  34 

Zygospira  modesta,  87 


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